.;it'iit1 


HOSS.   MOREWEDGE 

P.  O.  Box  2734 

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LIBRARY 

THE  UNIVERSITY 
OF  CALIFORNIA 

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PRESENTED  BY 

HOSSEINE  MOREWEDGE 


/'  / 


THE  RATE   OF  INTEREST 


THE  MACMILLAN  COMPANY 

KEW  YORK   •    BOSTON    -    CHICAGO 
ATLANTA   •    SAN    FRANCISCO 

MACMILLAN  &  CO.,  Limited 

LONDON   •    BOMBAY   •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  Ltd. 

TORONTO 


THE    RATE    OF  INTEREST 


ITS    NATURE,   DETERMINATION   AND 

RELATION  TO   ECONOMIC 

PHENOMENA 


BY 

IRVING   FISHER,   Ph.D. 

PROFESSOR   OF   POLITICAL   ECONOMY,   YALE   UNIVERSITY 


THE   MACMILLAN   COMPANY 

1907 

All  rights  reserved 


Copyright,  1907, 
By  the  MACMILIAN  COMPANY. 


Set  up  and  printed.     Published  October,  1907. 


NottoooD  JPrtzB 

J.  8.  Gushing  Co.  —  Berwick  &  Smith  Co. 

Norwood,  Mass.,  U.S.A. 


TO 

9rf)e  fRemorg 

OF 

JOHN    RAE 

WHO  LAID  THE   FOUNDATIONS 

;    UPON  WHICH 

I  HAVE  ENDEAVORED 

TO  BUILD 


PREFACE 

The  problem  of  interest  has  engaged  the  attention  of 
writers  for  two  thousand  years,  and  of  economists  since 
economics  began.  And  yet,  with  the  exception  of  what 
has  been  accomplished  by  Rae,  Bohm-Bawerk,  Landry, 
and  some  others,  very  little  progress  has  been  made  toward 
a  satisfactory  solution.  Even  these  writers  can  scarcely 
claim  to  have  established  a  definitive  theory  of  interest. 
While  the  value  of  their  work  is  great,  it  is  chiefly 
negative.  They  have  cleared  the  way  to  a  true  theory 
by  removing  the  confusions  and  fallacies  which  have 
beset  the  subject,  and  have  pointed  out  that  the  rate 
of  interest  is  not  a  phenomenon  restricted  to  money 
markets,  but  is  omnipresent  in  economic  relations. 

The  theory  of  interest  here  presented  is  largely  based 

upon  the  theories  of  the  three  writers  above  mentioned, 

and  may  therefore  be  called,  in  deference  to  Bohm-Bawerk, 

an  "agio  theory."     But  it  differs  from  former  versions 

of  that  theory  by  the  introduction  explicitly  of  an  income 

concept.     This  concept,  which  I  have  developed  at  length 

in  The  Nature  of  Capital  and  Income,  is  found  to  play  a 

central  role  in  the  theory  of  interest.     The  difficult  problem 

is  not  whether  the  rate  of  interest  i%  an  agio,  or  premium,  for 

of  this  there  can  be  no  question,  but  upon  what  does  that 

agio  depend  and  in  what  manner?     Does  it  depend,  for 

instance,  on  the  volume  of  money,  the  amount  of  capital, 

the  productivity  of  capital,  the  "superior  productivity  of 

roundabout  processes,"   the  labor  of   the    capitalist,    the 

helplessness  of  the  laborer,  or  upon  some  other  condition  ? 

vii 


viii  PREFACE 

The  solution  here  offered  is  that  the  rate  of  interest  de- 
pends on  the  character  of  the  income-stream,  —  its  size, 
composition,  probability,  and  above  all,  its  distribution 
in  time.  It  might  be  called  a  theory  of  prospective  provi- 
sion of  income. 

As  in  The  Nature  of  Capital  and  Income^  mathematics 
have  here  been  relegated  to  appendices.  These  appendices 
are  not,  however,  mere  translations  into  mathematical 
language  of  the  theory  verbally  expressed  in  the  text. 
Mathematics  can  properly  claim  no  place  in  economic 
discussions  except  as  they  add  something  not  expressible, 
or  at  any  rate  only  imperfectly  expressible,  in  ordinary 
language. 

Parts  of  Chapters  V  and  XIV  with  their  appendices 
have  appeared  in  somewhat  different  forms  in  Apprecia- 
tion and  Interest.  My  thanks  are  due  to  the  American 
Economic  Association  for  permission  to  use  portions  of 
this  monograph  unaltered.  Since  it  appeared  a  decade 
ago,  the  view  expressed  in  it,  to  the  effect  that  apprecia- 
tion of  money  should,  and  to  some  extent  does,  lower  the 
rate  of  interest  expressed  in  money,  has  gained  con- 
siderable currency,  though  it  is  still  unfamiliar  to  most 
persons.  It  has  been  thought  wise  to  present  again  the 
statistical  evidence  in  its  favor,  and  to  bring  the  statis- 
tics down  to  date. 

In  the  preparation  of  this  book  I  have  received  impor- 
tant aid  from  many  persons.  For  general  criticism  I  am 
indebted  to  my  wife,  to  my  colleagues.  Professors  H.  C. 
Emery  and  J.  P.  Norton,  and  to  my  friend  Richard  M. 
Hurd,  President  of  the  Mortgage-Bond  Company  of  New 
York  City.  My  thanks  are  also  due  to  Finance  Minister 
Bohm-Bawerk  for  his  kindness  in  reading  and  criticising 
the  chapter  devoted  to  his  theory  of  interest ;  to  Professor 
Clive  Day  for  facts  and  references  on  the  history  of  inter- 
est rates ;  to  Dr.  Lester  W.  Zartman  for  a  large  part  of 


PKEFACE  IX 

the  statistical  computation  and  for  many  helpful  criti- 
cisms ;  to  two  of  my  students,  Mr.  Harry  G.  Brown  and 
Mr.  J.  H.  Parmelee,  for  valuable  aid  in  proof-reading, 
including  many  keen  and  fruitful  suggestions  ;  and  to 
my  brother,  Herbert  W.  Fisher,  for  a  most  searching 
and  valuable  criticism    of  the   mode    of  expression  and 

exposition. 

IRVING  FISHER. 
New  Haven,  July,  1907. 


CONTENTS 
FIKST  SUMMARY 

CHAPTERS 

PART       I.  CRITICISM   OF  PREVIOUS  THEORIES       .           I-IV 

PART     II.  FIRST  APPROXIMATION        ....        V-VII 

PART  III.  SECOND  AND    THIRD  APPROXIMATIONS    VIII-XI 

PART  IV.     CONCLUSIONS XII-XVII 


XI 


xii  CONTENTS 


SECOND   SUMMARY 
PART   I.     CRITICISM   OF   PREVIOUS   THEORIES 

OHAPTER  PAOB 

I.     Crude  Theories 3 

II.     Productivity  Theories      .......  10 

III.  Cost  Theories 29 

IV.  Bohm-Bawerk's  Theory 53 

PART   II.     FIRST   APPROXIMATION 

V.     Appreciation  and  Interest      .....  77 

VI.     Time-pkeference 87 

VII.     First  Approximation  (Rigid  Income)      ....  117 

PART  III.     SECOND  AND  THIRD  APPROXIMATIONS 

VIII.     Second  Approximation  (Flexible  Income)     .         .         .  137 

IX.     Classes  of  Options 178 

X.     Invention 198 

XI.     Third  Approximation  (Uncertain  Income)     .        .  207 

PART  IV.     CONCLUSIONS 

XII.     Role  of  Interest  in  Economic  Theory  ....  225 

XIII.  Application  to  Actual  Conditions  .....  236 

XIV.  Inductive  Verification  (Monetary)        ....  257 
XV.     Inductive  Verification  (Economic)         ....  289 

XVI.     Inductive  Refutation  of  "Money  Theory"          .         .  317 

XVII.     Summary 327 

Glossary 337 

APPENDICES 345 

INDEX 429 


ANALYTICAL  TABLE  OF  CONTENTS 


CHAPTER   I 
Crdde  Theories 

PAGE 

§  1.   Introduction 3 

§  2.   Early  theories 4 

§  3.    "  Supply  and  demand  "  theory 6 

§4.    "  Use  of  money  "  theory 7 


CHAPTER   II 


Pkoductivitt  Theories 


§  1.  Distinction  between  explicit  and  implicit  interest    . 

§  2.  Turgot's  productivity  theory  based  on  land 

§  3.  Common  form  of  productivity  theory 

§  4.  True  sequence :  capital-goods,  income-services,  income-value 
capital-value  ....... 

§  5.  To  increase  productivity  will  not  increase  interest    . 

§  6.  Case  of  ten  replaceable  machines  examined 

§  7.  The  same  when  the  rate  of  interest  is  zero 

§  8.  Reproductivity  theory  of  Del  Mar  and  Henry  George 

§  9.  Example  of  growing  timber 

§  10.  Conclusions 


10 
11 
12 

14 
15 
16 
20 
22 
23 
28 


CHAPTER   III 


Cost  Theories 


§  1.    Cost  theories  overlook  the  fact  that  cost  is  usually  discounted 

return 29 

§  2.    Case  when  rate  of  return  on  cost  exceeds  rate  of  interest         .       31 
§  3.    Roscher's  fishing  net,  where  sacrifice  and  return  are  both 

measured  in  fish  .........       33 

§4.    Theory  that  capital  "  saves  labor  " 35 

§  5.    Case  where  sacrifice  and  return  are  both  measured  subjectively      36 

xiii 


xiv  ANALYTICAL   TABLE   OF   CONTENTS 

PAOB 

§  6.    Socialist  exploitation  theory,  correct  in  claim  that  value  ex- 
ceeds cost 38 

§  7.    Socialist  theory  incorrect  in  claim  that  laborers  are  defrauded  40 
§  8.   Theory  that  interest  is  wages  of  labor  of  "  managing  "  capital  42 
§  9.    Abstinence  theory.     "Labor  of  waiting"  not  a  true  cost,  be- 
cause not  discounted 43 

§  10.   Answer  that  no  costs  need  be  discounted,  examined        .         .  45 
§  11.    If  the  answer  be  accepted,  capital-value  is  equal  to  its  expected 

income ...........  48 

§  12.    Interest  is  not  a  cost  of  production 50 

§  13.   Summary 51 


CHAPTER   IV 
Bohm-Bawerk's  Theory 

§  1.  Statement  of  Bohm-Bawerk's  agio  theory  of  interest  .  .  53 
§  2.    Criticism  of  Bohm-Bawerk's  concept  of  an  average  production 

period  ...........       55 

§  3.    Statement  of  Bohm-Bawerk's  theory  of  "  technical  superiority 

of  present  over  future  goods  " 58 

§  4.    Error  of  Bohm-Bawerk  in  ascribing  to  "  teclinical  superiority  " 

of  present  goods,  effects  actually  due  to  other  factors,  viz. 

underestimation  of  and  overprovision  for  future  .         .       61 

§  5.  Error  best  seen  by  supposing  these  other  factors  absent .  .  63 
§  6.    Error  made  still  clearer  if  we  suppose  increase  of  productivity 

not  to  go  on  indefinitely        .......       68 

§  7.    Final  criticisms 71 


CHAPTER   V 
Appreciation  and  Interest 

§  1.    The  rate  of  interest  dependent  on  monetary  appreciation  or 

depreciation 77 

§  2.  Appreciation  or  depreciation,  to  affect  interest,  must  be  fore- 
seen       78 

§  3.    Relation  between  interest  and  appreciation  or  depreciation 

illustrated 80 

§  4.  Case  where  interest  and  appreciation  are  compounded  mo- 
mently   81 

§  5.    Limits  imposed  on  rates  of  interest  in  two  standards  and  the 

appreciation  between  them 82 

§  6.   There  is  no  "  absolute  "  interest  in  some  "  absolute  "  standard      84 


ANALYTICAL   TABLE   OF   CONTENTS 


XV 


CHAPTER  VI 


TiME-PREFERENCK 

§  1.    "  Time-preference  "  is  a  particular  species  of  "  desirability  " 
§  2.    This  preference  applies  to  all  goods,  but  in  the  last  analysis 

only  to  final  income 

§  3.   The  rate  of  interest  enters  into  all  prices  except  the  price  of 

final  services         ........ 

§  4.   Time-preference  depends  on  income         .... 

§  5.    Time-preference  depends  on  size  of  income 

§  6.   Time-preference  depends  on  time-shape  of  income  . 

§  7.    Time-preference  depends  on  composition  of  income 

§  8.    Time-preference  depends  on  probability  of  income  . 

§  9.    The  character  of  the  dependence  of  time-preference  on  income 

varies  with  five  human  characteristics  .... 

§  10.    Summary 

§  11.   Shortcomings  of  statement  that  interest  depends  on  abundance 

of  capital       ......... 

§  12.    Schedule  of  relation  between  time-preference  and  income 


87 

89 

90 
92 
94 
95 
98 
99 

102 
109 

109 
113 


CHAPTER   VII 

First  Approximation  to  the  Theory  of  Interest 
(assuming  Income  Rigid) 

§  1.    Introductory 117 

§  2.    Equalization  of  individual  rates  of  preference,  by  borrowing 

and  lending  .         .         .         .         .         .         .         .         .         .118 

§  3.    Diagrammatic  illustration         .......  120 

§  4.    Equalization  of  preference  rates  by  buying  and  selling    .        .  125 

§  5.    Futility  of  socialistic  suppression  of  interest    ....  127 

§  6.    Equalization  of  preference  rates  means  maximizing  "desira- 
bility"            129 

§  7.   Formulation   of    the  first   approximation   to    the   theory  of 

interest 130 


CHAPTER   VIII 

Second  Approximation  to  the  Theory  of  Interest 
(assuming  Income  Flexible) 

§  1.    Introductory 137 

§  2.    Choice  of  optional    income-streams   depends   on   maximum 

present  value 139 

§  3.    Any  resulting  inconvenience  in  time-shape  of  income  may  be 

offset  by  borrowing  or  lending 141 

§  4.   A  change  in  the  rate  of  interest  produces  a  change  in  choice  .  145 


XVI 


ANALYTICAL   TABLE   OF   CONTENTS 


§  5.    Although  interest  depends  on  income-stream,  and  the  choice 
of  income-stream  depends  on  interest,  yet  interest  is  deter- 
minate ...........     147 

§  6.    Statement  of  the  interest-determining  condition  relating  to 

optional  employments  of  capital  .....     149 

§  7.    A  second  method  of  stating  this  interest-determining  condition     150 
§  8.    A  third  method  of  stating  this  interest-determining  condition      152 
§  9.    The  third  method,  when  the  range  of  choice  is  infinite.     Mar- 
ginal rate  of  return  on  sacrifice  equals  the  rate  of  interest  .     156 
§  10.    Similarity  to  llae's  theory  that  instruments  are  "  wrought  up  " 
to  a  point  corresponding  to  the  "effective  desire  of  accu- 
mulation."    Landry's  theory 159 

§  11.   The  relation  of  the  author's  theory  to  Henry  George's  theory      161 
§  12.    The  relation  of  the  author's  theory  to  Bohni-Bawerk's  theoi-y      163 
§  13.    Summary  of  relation  of  author's  theory  to  previous  theories   .     164 
§  14.    Range  of  choice  (as  well  as  the  choice  itself)  depends  on  rate 

of  interest     ..........     167 

§  15.    But  this  fact  does  not  materially  affect  the  statement  of  the 

theory 171 

§  16.    Tlie  existence  of  a  range  of  choice  prevents  wide  fluctuations 

in  the  rate  of  interest 175 


CHAPTER   IX 


Classes  of  Options 

§  1.  Three  groups  of  options 

§  2.  Options  as  to  time  of  using  capital   . 

§  3.  The  effect  of  the  slowness  of  Nature  on  interest 

§  4.  The  effect  of  the  productivity  of  Nature  on  interest 

§  5.  Case  of  perishable  goods  . 

§  6.  Case  of  renewable  goods  . 

§  7.  Case  of  repairs  and  betterments 

§  8.  Case  of  optional  methods  of  production 

§  9.  Case  of  optional  employments  of  labor 

J  10.  Selection  of  option  varies  with  rate  of  interest 


178 
180 
185 
186 
187 
188 
190 
101 
193 
195 


CHAPTER   X 
Invention 


§  1.    Inventions  widen  range  of  choice  of  alternative  income-streams  198 

§  2.    Inventions  depress  present  income  and  raise  future  income     .  199 
§  3.   Effect   of   invention   on   interest   not  registered   by  insiders' 

profits 201 

§  4.    Inventions  raise  interest  only  temporarily        ....  203 

§  5.    Conditions  which  facilitate  invention 204 


ANALYTICAL  TABLE   OF   CONTENTS  xvii 


CHAPTER   XI 

Third  Approximation  to  the  Theory  of  Interest 
(assuming  Income  Uncertain) 

PAGE 

§  1.    Possibilities  of  borrowing  and  lending  limited  by  necessity  of 

giving  security 207 

§  2.  One  consequence  is  divergences  in  rates  of  preference,  inter- 
est, and  return  on  sacrifice 210 

§  3.    Another  consequence  of  risk  is  variation  in  duration  of  loans      211 

§  4.    Another  consequence  of  risk  is  divergence  between  expected 

and  realized  return 212 

§  5.    Effect  of  risk  on  rate  of  interest  on  riskless  loans    .         .         .     213 

§  6.    Differentiation  of  risky  and  safe  investments  and  investors, 

bonds  and  stocks 215 

§  7.  Effect  of  the  introduction  of  element  of  risk  upon  the  interest- 
determining  conditions 217 

jS  8.    Summary 220 


CHAPTER  Xll 

Role  of  Interest  in  Economic  Theory 

§  1.    The  interest  rate  plays  a  role  in  determining  the  prices  of 

capital 225 

§  2.   The  interest  rate  plays  a  r61e  in  determining  the  prices  of 

general  services 226 

§  3.   The  interest  rate  plays  a  role  in  determining  wages  in  particular  228 
§  4.    The  problem  of  distribution  usually  misconceived  .         .         .  229 
§  5.    The  interest  rate  plays  a  role  in  distribution    ....  231 
§  6.    Inequality  in  distribution  of  capital  due  to  opportunity  to  ex- 
change income 234 

■'  CHAPTER   XIII 

Application  to  Actual  Conditions 


§  1.   Application  of  the  theory  of  interest  to  personal  loans    . 

§  2.    Application  of  the  theory  of  interest  to  public  loans 

§  3.   Application  of  the  theory  of  interest  to  business  loans  in 

general  ......... 

§  4.    Application  of  the  theory  of  interest  to  short-term  loans 

§  5.    Application  of  the  theory  of  interest  to  long-term  loans  , 

§  6.    Business  loans  not  "productive"  except  as  they  enable  mer 

chants  to  choose  "  productive  "    options 
§  7.    Classification  of  loans 


236 

238 

240 
242 
244 

246 
252 


xviii  ANALYTICAL  TABLE   OF  CONTENTS 

PAGK 

§  8.    Interplay  between  borrowers  and  lenders         ....     253 

§  9.   Sale  of  loans  before  maturity 264 

§  10.    Explicit  and  implicit  interest.     Risk        .         .  .        .     265 

CHAPTER   XIV 
Inductive  Verification  (Monetary) 

§  L    Appreciation  is  foreseen  under  the  disguise  of  changes  in  prices    257 
§  2.    Statistical    evidence    from    simultaneous    loan    contracts  in 

United  States  "  coin  "  and  "  currency  "  ....  258 
§  3.  Measure  of  foreseen  appreciation  based  on  preceding  evidence  261 
§  4.  Evidence  from  India  "  rupee  paper  "  and  gold  bonds  .  .  265 
§  5.  Evidence  from  price-movements  and  interest  in  England  .  270 
§  6.    Evidence  from  price-movements  and  interest  in   Germany, 

France,  and  the  United  States 273 

§  7.    Evidence  from  price-movements  and  interest  in  India,  Japan, 

and  China 276 

§  8.   Proof  that  interest  does  not  fully  adjust  itself  to  monetary 

changes 277 

§  9.    Errors  due  to  mistaking  high  or  low  rates  in  money  for  rates 

absolutely  high  or  low 280 

§  10.    When  long  periods  of  time  are  taken,  the  relation  between 

appreciation  and  interest  is  more  definite     ....     282 
§  11.    Manner  in  which,  in  any  price-movement,  the  rate  of  interest 

is  gradually  adjusted 284 

§12.    Application  to  theory  of  "  credit  cycles "         ....     285 
§  13.    Conclusions 287 


CHAPTER   XV 

Inductive  Verification  (Economic)  •• 

§  1.    Similar  significance  of  low  interest,  lending,  accumulation, 

and  durability  of  instruments 289 

§  2.    Where  foresight,  self-control,  and  regard  for  posterity  are 

present,  interest  tends  to  be  low 290 

§  3.  In  some  of  these  cases  other  explanations  may  enter  .  .  294 
§  4.  Disregard  of  posterity  during  decline  of  Roman  Empire  .  .  296 
§  5.    Foresight,  self-control,  and  regard  for  posterity  partly  natural 

and  partly  acquired 297 

§  6.  Where  incomes  are  low,  interest  tends  to  be  high  ..  ,  .  299 
§  7.    Where  incomes  are  low  in  the  food  elements,  interest  tends  to 

tehigh 301 

§  8.    Where  incomes  are  risky,  commercial  interest  tends  to  be 

high,  riskless  or  pure  interest  low,  and  reversely  .  .  302 
§  9.   Where  incomes  are  ascending,  interest  tends  to  be  high  ;  case 

of  United  States 304 


ANALYTICAL  TABLE   OF  CONTENTS 


XIX 


§  10.  Ditto,  case  of  particular  parts  of  United  States 

§  11.  Ditto,  case  of  other  countries  .... 

§  12.  Ditto,  case  of  misfortune  and  invention  . 

§  13.  Ditto,  case  of  rhythmic  changes  in  income 

§  14.  Summary 


PA.OB 

306 
309 
311 
314 
316 


CHAPTER  XVI 
Inductive  Refutation  of  "Money-theory" 

§  1.    Statistical  refutation  of  money-theory  necessary  for  business 

man 317 

2.  Table  giving  rate  of  interest  in  relation  to  price-level        .'        .  318 

3.  Table  giving  rate  of  interest  in  relation  to  money  per  capita     .  320 

4.  Relation  of  bank  reserves  to  rate  of  interest  explained      .         .  322 

5.  Case  of  panics .  324 


CHAPTER  XVII 
Summary 


§  1.  Appreciation  and  interest 

§  2.  Enumeration  of  interest-determining  conditions 

§  3.  Possible  future  changes  in  range  of  choice 

§  4.  Possible  future  changes  in  character  of  man 

§  5.  The  element  of  fashion  as  a  factor  in  determining  interest 

§  6.  Conclusion 

GLOSSARY 
Definitions  of  Technical  Terms  Used         .... 


327 
328 
329 
331 
332 
334 


337 


APPENDICES 


Appendix  to  Chapter  II.     Productivity  Theories 


PAGE 


§  1  (to  Ch.  II,  §  6).  Mathematical  proof  that  the  rate  of  net  in- 
come from  reconstituted  capital  is  equal  to  the  rate  of  inter- 
est employed  in  valuing  the  elements  of  which  it  is  composed    347 

§  2  (to  Ch.  11,  §  7).  Discussion  of  the  case  of  zero  interest  as  ap- 
plied to  the  valuation  of  reconstituted  capital        .        .        .     349 


Appendix  to  Chapter  IV.    Bohm-Bawerk's  Theory 

§  1  (to  Ch.  IV,  §  2).  Nature  of  various  means,  —  arithmetical,  geo- 
metrical, harmonical,  etc 351 

§  2  (to  Ch.  IV,  §  2).     Case  illustrating  futility  of  measuring  average 

production  period 352 

§  3  (to  Ch.  IV,  §  3).      Showing  how   periods  of  production  which 

are  relatively  long  but  unproductive  are  eliminated       .         .     353 

§  4  (to  Ch.  IV,  §  4).  Mathematical  refutation  of  Bohm-Bawerk's 
claim  as  to  ground  of  preference  for  present  over  future  in- 
vestment of  labor 354 


Appendix  to  Chapter  V.     Appreciation  and  Interest 

§  1  (to  Ch.  V,  §  2).     History  of  theory  of  appreciation  and  interest     356 
§  2  (to  Ch.  V,  §  3).     Formula  connecting  the  rates  of  interest  in 

two  diverging  standards 358 

§  3  (to  Ch.  V,  §  4).     Formulae,  when  rates  of  interest  and  of  appre- 
ciation are  reckoned  oftener  than  yearly        ....     360 
§  4  (to  Ch.  V,  §  5).     Case  of  partial  payments  ....     361 

§  5  (to  Ch.  V,  §  5).     Formulae  for  cases  of  compound  interest  and 

partial  payments 363 

§  6  (to  Ch.  V,  §  5).  Case  of  separate  payments  of  interest  and 
principal  in  one  of  the  two  standards  and  equivalent  pay- 
ments in  the  other 365 

§  7  (to  Ch.  V,  §  5).     Case  of  separate   payments   of  interest  and 

principal  in  both  standards 366 

§  8  (to  Ch.  V,  §  5).     Case  of  perpetual  annuity        ....     367 
§  9  (to  Ch.  V,  §  5).     Case  in  which  the  rate  of  appreciation  changes 

each  year •        .     369 

xxi 


xxii  ANALYTICAL  TABLE   OF   CONTENTS 

Appendix  to  Chapter  VIL     First  Approximation 

PAGE 

§  1.   Mathematical   statement  of  the  four  conditions  determining 

interest  rate,  when  two  years  only  are  considered  .  .  374 
§  2.  The  number  of  equations  is  equal  to  the  number  of  unknowns  376 
§  3.   Transformation  of  formulae  for  explicit  determination  of  rate 

of  interest 377 

§  4.    Extension  of  the  mathematical  statement  to  apply  to  m  years     380 
§  5.    Reasons  for  steadiness  of  interest  rates  from  year  to  year       .     383 
§  6.    The  condition  that  rates  of  time-preference  shall  equal  the 
rate  of  interest  is  equivalent  to  the  condition  that  "total 

desirability  "  shall  be  a  maximum 385 

§  7.  Geometrically  interpreted,  the  condition  of  maximum  desira- 
bility is  fulfilled  at  the  point  of  tangency  of  an  iso-desirabil- 
ity  curve  and  a  straight  line  the  slope  of  which  corresponds 

to  the  rate  of  interest 387 

§  8.  The  same  geometrical  construction  interprets  equality  of  time- 
preference  and  interest  rate 390 

§  9.   Extension  from  two  to  three  or  more  years     ....     392 
§  10.    Geometrical  solution  of  the  rate  of  interest      ....     394 

Appendix  to  Chapter  VIII.     Second  Approximation 

§  1.  The  equations  of  the  first  approximation  repeated  and  re- 
adapted         395 

§  2.  The  new  equations  peculiar  to  the  second  approximation  .  397 
§  3.    Geometrical  representation  in  two  dimensions  of  the  range 

of  choice 402 

§  4.    Geometrical  representation  of  the  determination  of  choice  for 

a  given  rate  of  interest 405 

§  5.    Extension  to  three  and  more  dimensions          ....  407 
§  6.    Geometrical  determination  of  the  rate  of  interest    .         .         .  408 
§  7.   The  condition  of  maximum  desirability  includes  that  of  maxi- 
mum present  value 411 

§  8.   Summary 412 

Appendix  to  Chapter  XI.     Third  Approximation 

§  1  (to  Ch.  XI,  §  8).    Reasons  for  omitting  mathematical  statement 

of  third  approximation 416 

Appendix  to  Chapter  XIV.     Statistical  Data 

§  1.  Table  of  interest  rates  each  year  in  seven  countries  .  .  418 
§  2.  References  to  other  statistics  of  the  rate  of  interest  .  .421 
§  3.    Index-numbers  of  prices 425 

INDEX 429 


>* 


PART  I.     Criticism 

Chapter      I.  Crude  Theories 

Chapter     II.  Productivity  Theories 

Chapter  III.  Cost  Theories 

Chapter   IV.  Bohm-Bawerk's  Theory 


THE  RATE  OF  INTEREST 

CHAPTER  I 

CRUDE   THEORIES 
§1 

If  the  theory  to  be  presented  in  this  book  is  correct,  the 
rate  of  interest  in  any  community  is  an  index  of  the 
preference,  in  that  community,  for  a  dollar  of  present 
over  a  dollar  of  future  income.  The  task  of  justifying 
this  theory  will  be  facilitated  by  a  brief  preliminary  review 
of  rival  theories.  A  complete  history  of  theories  of  interest 
has  been  made  unnecessary  by  Bohm-Bawerk's  admirable 
Capital  and  Interest}  For  the  same  reason,  it  is  not  neces- 
sary to  combat  many  of  the  special  theories  advanced  by 
individual  writers.  The  theories  which  are  here  selected 
for  criticism  are  for  the  most  part  those  which  have  the 
greatest  currency,  either  in  economic  literature  or  in  the 
unexpressed  but  none  the  less  firmly  rooted  ideas  of  busi- 
ness or  professional  men.  Experience  shows  that  nearly 
every  student  of  economic  science  has  almost  imconsciously 
acquired  a  number  of  crude  and  usually  false  ideas  on  this 
important  subject.  Such,  for  instance,  is  the  idea  that 
interest  is  the  price  paid  for  the  ''use  of  money";  or  that 
it  represents  the  "productivity"  of  capital  or  the  "fecun- 
dity" of  plants  and  animals;    or  that  it  represents  some 

*  English  translation  by  Smart,  (Macmillan)  1890.  See  also  Recent 
Literature  on  Interest,  English  translation  by  Scott  &  Feilbogen,  (Mac- 
millan) 1903. 

3 


4  THE   RATE   OF  INTEREST  [Chap.  I 

"cost"  to  the  producer,  such  as  the  cost  of  the  capitaHst's 
personal  exertion  in  controlHng  capital,  or  the  "cost  of 
waiting";  or  that  it  constitutes  a  species  of  legalized  plun- 
der perpetrated  by  the  employer  on  the  employed.  Be- 
fore the  correct  theory  of  interest  can  be  securely  implanted 
in  any  mind,  these  ideas  must  first  be  eradicated.  To 
accomplish  this  is  the  object  of  the  present  and  of  the 
next  three  chapters.^ 

§2 

An  objection,  formerly  common,  to  the  practice  of  taking 
interest  was  that  interest  is  "  unnatural."  The  word  em- 
ployed among  the  Greeks  to  signify  interest  or  usury  was 
T0/C09,  "offspring";  and  Aristotle  declaimed  against  the 
taking  of  interest,  on  the  ground  that  money  could  not 
have  "offspring," — a  curious  instance  of  the  influence  of 
terminology  on  thought. 

Interest-taking  between  Jews  was  forbidden  by  the 
Mosaic  laws,  and  similarly,  in  Rome,  interest-taking  be- 
tween Romans  was  prohibited.  Many  biblical  texts  show 
the  hostile  attitude  of  the  writers,  both  in  the  Old  and  New 
Testaments,  toward  the  practice,  and  the  Church  Fathers 
through  the  Middle  Ages  for  over  a  thousand  years  waged 
a  ceaseless  but  fruitless  war  against  interest-taking.  St. 
Thomas  Aquinas  stated  that  interest  was  an  attempt  to 
extort  a  price  for  the  use  of  things  which  had  already  been 
used  up,  as  for  instance,  grain  and  wine.^  He  also  declared 
that  interest  constituted  a  payment  for  time,  and  that  time 
was  a  free  gift  of  the  Creator  to  which  all  have  a  natural 
right.' 

'  These  chapters  for  the  most  part  may  be  said  to  be  a  brief  epit- 
ome, under  a  changed  classification,  of  Bohm-Bawerk's  exhaustive 
Capital  and  Interest. 

^  This  criticism  against  the  legitimacy  of  interest  is  very  nearly  re- 
vived by  Bohm-Bawerk  in  his  criticism  of  the  modern  "  use  "  theory 
of  interest.     Op.  cit.,  Chap.  VIII. 

'  This  theory  is  not  unlike  one  of  the  objections  made  to  land-rent 
by  the  single- tax  advocates ;  namely,  that  space  is  a  free  gift  of  nature. 


Sec.  2]  CRUDE  THEORIES  6 

The  unpopularity  of  interest-taking  increased  until  the 
thirteenth  century;  but  the  practice  persisted,  and  as 
business  operations  increased  in  importance,  certain  exemp- 
tions and  exceptions  from  its  general  prohibition  were 
secured.  Pawnshops,  banks,  and  money-lenders  were 
specially  licensed,  and  permission  was  granted  for  buying 
annuities,  and  taking  land  on  mortgage  for  money  loaned. 
One  of  the  subterfuges  by  which  the  allowance  of  interest 
was  excused  suggests  the  true  idea  of  interest  as  an  index 
of  the  relative  preference  for  present  over  futm-e  goods. 
It  was  conceded  that,  whereas  a  loan  should  be  nominally 
without  interest,  yet  when  the  debtor  delayed  payment,  he 
should  be  fined  for  his  delay  {mora) ,  and  the  creditor  should 
receive  compensation  in  the  form  of  '^  inter  esse. ^^  Through 
this  loophole  it  became  common  to  make  an  understanding 
in  advance,  by  which  the  payment  of  a  loan  should  be  "de- 
layed" year  after  year,  and  with  every  such  postponement 
a  "fine"  should  become  payable. 

Some  of  the  Protestant  reformers,  while  not  denying  that 
interest-taking  was  wrong,  admitted  that  it  was  impossi- 
ble to  suppress  it,  and  that  it  should  therefore  be  tolerated. 
This  toleration  was  in  the  same  spirit  as  that  in  which 
many  reformers  to-day  defend  the  licensing  of  vicious 
institutions,  such  as  saloons,  racetracks,  lotteries,  and 
houses  of  prostitution. 

In  the  sixteenth  centm-y  interest-taking  began  to  find 
some  definite  champions.  Calvin  attempted  to  discrimi- 
nate between  interest-taking  which  was  right  and  interest- 
taking  which  was  wi'ong.  Among  the  wrong  kinds  he 
classed  the  taking  of  interest  from  the  poor  and  from  those 
in  urgent  need,  and  the  taking  of  interest  in  excess  of  a 
legal  maximum. 

In  order  to  defend  interest,  its  champions  began  to  con- 
struct theories  to  account  for  the  phenomenon.  Most  of 
these  early  theories  were  little  more  than  a  shifting  of  the 
problem.  It  was  seen  that  capital  earned  income  whether 
it  was  lent  or  not.     The  income  which  a  lender  obtains 


6  THE  RATE  OF  INTEREST  [Chap.  I 

through  a  loan  contract  may  be  called  explicit  interest;  but 
it  was  clear  that  the  borrower  was  enabled  to  pay  this 
interest  because  the  capital  which  he  borrowed  earned  it 
for  him.  The  income  which  capital  thus  earns  may  be 
called  implicit  interest.  The  earliest  attempt  to  construct 
a  theory  of  interest  merely  explained  explicit  interest  in 
terms  of  implicit  interest.  Salmasius  and  Locke,  both  in 
the  seventeenth  century,  attempted  thus  to  explain  in- 
terest. They  tried  to  justify  the  taking  of  interest  in  a 
loan  on  the  ground  that  an  equivalent  to  that  interest  was 
obtained  by  the  borrower  from  the  capital  he  borrowed, 
and  might  have  been  obtained  by  the  lender  of  the  capital 
had  he  retained  it.  If,  they  said,  a  man  lends  $1000, 
he  is  entitled  to  interest  upon  it  because,  had  he  used 
it  in  business  himself,  he  could  have  made  profits  by  means 
of  it.  But  beyond  the  bare  statement  that  unlent  capital 
yields  income,  these  theories  did  not  go.  The  real  prob- 
lem—  "  why  capital  yields  income  to  the  user"  — was  left 
untouched. 

§3 

The  theories  just  described  are  for  the  most  part  obsolete 
to-day;  yet  we  have  a  number  of  other  theories  almost 
equally  crude.  If  a  modern  business  man  is  asked  what 
determines  the  rate  of  interest,  he  may  usually  be  expected 
to  answer,  ''the  supply  and  demand  of  loanable  money." 
But  "supply  and  demand"  is  a  phrase  which  has  been  too 
often  forced  into  service  to  cover  up  difficult  problems. 
Even  economists  have  been  prone  to  employ  it  to  describe 
economic  causation  which  they  could  not  unravel.  It  was 
once  wittily  remarked  of  the  early  wi-iters  on  economic 
problems,  "Catch  a  parrot  and  teach  him  to  say  'supply 
and  demand,'  and  you  have  an  excellent  economist.'' 
Prices,  wages,  rent,  interest,  and  profits  were  thought  to 
be  fully  "explained"  by  this  glib  phrase.  It  is  true  that 
every  ratio  of  exchange  is  due  to  the  resultant  of  causes 


Sec.  4]  CRUDE  THEORIES  7 

operating  on  the  buyer  and  seller,  and  we  may  classify 
these  as  "demand"  and  "supply."  But  this  fact  does  not 
relieve  us  of  the  necessity  of  examining  specifically  the  two 
sets  of  causes,  including  utility  in  its  effect  on  demand,  and 
cost  in  its  effect  on  supply.  Consequently,  when  we  say 
that  the  rate  of  interest  is  due  to  the  supply  and  demand 
of  "capital"  or  of  "money"  or  of  "loans,"  we  are  very  far 
from  having  an  adequate  explanation.  It  is  true  that 
when  merchants  seek  to  discount  bills  at  a  bank  in  large 
numbers  and  for  large  amounts,  the  rate  of  interest  will 
tend  to  be  high,  and  that  when  merchants  do  not  apply  in 
large  numbers  and  for  large  amounts,  the  rate  of  interest 
will  tend  to  be  low.  But  we  must  inquire  for  what  pm-poses 
and  from  what  causes  merchants  thus  apply  to  a  bank  for 
the  discount  of  loans,  and  why  it  is  that  some  apply  to  the 
bank  for  loans  and  others  supply  the  bank  with  the  funds 
to  be  loaned.  The  real  problem  is :  What  causes  make  the 
demand  for  loans,  and  what  causes  make  the  supply  ?  This 
question  is  not  answered  by  the  summary  "  supply  and  de- 
mand" theory.  The  explanation  is  not  simply  that  those 
who  have  much  capital  supply  the  loans  and  those  who 
have  little  capital  demand  them.  In  fact,  the  contrary  is 
quite  often  the  case.  The  depositors  in  savings  banks  are 
the  lenders,  and  they  are  usually  poor,  whereas  those  to 
whom  the  savings  bank  in  turn  lends  the  fimds  are  rela- 
tively rich. 

§4 

There  is  another  phrase  often  employed  by  business 
men  to  explain  the  rate  of  interest  or,  at  all  events,  its 
existence.  It  is  often  said  that  interest  is  the  price  paid 
for  the  "use  of  money."  As  an  explanation  this  is  almost 
as  superficial  as  "supply  and  demand  " ;  for  it  is  clear  that 
the  "use"  of  money  is  to  facilitate  exchange,  and  that,  ex- 
cept in  rare  instances  (as  when  a  bank  borrows  a  chest  of 
gold  to  reinforce  its   cash  reserve),  the  money  borrowed 


8  THE  RATE  OF  INTEREST  [Chap.  I 

does  not  remain  long  in  the  hands  of  the  borrower.  If 
interest  is  a  payment  for  use,  it  is  payment  for  the  use,  not 
of  the  borrowed  money,  but  of  that  for  which  the  borrowed 
money  is  expended.  For  this  reason  the  final  explanation 
of  the  rate  of  interest  is  not  to  be  sought  in  any  monetary 
cause. 

A  special  version  of  the  theory  that  interest  depends  on 
the  "use  of  money"  is  found  in  the  very  persistent  belief 
that  the  quantity  of  money  in  circulation  governs  the  rate 
of  interest,  — that  the  rate  is  high  when  money  is  scarce, 
and  low  when  money  is  plentiful.  The  shallowness  of  this 
theory  has  been  exposed  repeatedly  by  economists  from  the 
time  of  Hume  to  the  present.  It  requires  only  a  little  reflec- 
tion to  see  that,  although  an  increase  of  the  quantity  of 
money  in  circulation  will  increase  the  supply  of  loans,  it 
will  also  equally  increase  the  demand.  For  instance,  a 
piano  dealer  who  borrows  $10,000  in  order  that  he  may  add 
to  his  stock  in  trade  50  pianos  costing  $200  apiece  would, 
if  the  supply  of  money  were  doubled,  require  a  loan  of 
double  the  amount;  for  such  an  inflation  of  the  currency 
would  double  the  cost  of  his  stock,  and  in  order  to  obtain 
50  pianos  —  costing  now  $400  apiece  instead  of  $200  — 
he  would  have  to  borrow  $20,000  instead  of  $10,000. 

In  spite  of  such  reasoning,  showing  that  an  inflation  of 
the  currency  must  act  on  the  demand  for  loans  as  surely 
as  upon  the  supply,  the  theory  that  an  abundance  of  money 
lowers  the  rate  of  interest  is  nevertheless  widely  accepted 
even  among  intelligent  business  men.  Yet  facts  do  not, 
any  more  than  a  priori  reasoning,  lend  support  to  this 
belief.^ 

The  probable  reason  for  the  persistence,  among  business 
men,  of  the  opinion  that  an  abundance  of  money  reduces 
the  rate  of  interest  is  the  observed  fact  that  the  rate  of 
interest  is  high  when  the  reserves  in  banks  are  low,  and 
vice  versa,  and  that  the  rate  in  a  loan  center  can  be  materi- 
ally reduced  by  bringing  to  that  center  a  supply  of  actual 
*  A  statistical  discussion  is  contained  in  Chap.  XVI,  infra. 


Sec.  4]  CRUDE  THEORIES  9 

money  to  relieve  the  "stringency."  This  is  true,  and  it  is 
not  denied  that  money  plays  a  part  in  determining  the 
rate  of  interest.  But  the  part  which  it  plays  is  chiefly 
as  a  puppet  of  other  and  mightier  factors.  The  funda- 
mental causes  at  work  in  a  " money"  market  are  not  mone- 
tary at  all,  but  economic.  The  economic  causes  operate 
through  money  and  seldom  show  themselves  save  under  a 
money  disguise;  but,  generally  speaking,  money  is  only 
their  instrument,  not  an  independent  factor.  If  money  is 
plentiful  for  loan  piu-poses,  it  is  because  its  owners  decide 
to  apply  it  for  these  rather  than  for  other  purposes, 
and  not  because  money  in  general  is  plentiful.  The  owners 
of  money  determine  the  purpose  to  which  it  shall  be  applied. 
To  imderstand  the  real  causes  at  work  in  the  loan  market, 
we  must  go  back  of  the  money  itself  and  learn  the  reasons 
for  bringing  it  into  that  market  instead  of  spending  it  in 
other  markets,  —  the  meat,  fish,  fruit,  or  grocery  markets, 
for  instance.  The  abimdance  or  scarcity  of  money  for 
loan  purposes  is  merely  a  sign  or  symptom  of  those  more 
fundamental  causes  operating  upon  the  rate  of  interest. 

A  full  consideration  of  the  manner  in  which  money  in  loan 
centers  is  related  to  the  rate  of  interest  must,  however,  be 
deferred  to  Chapters  V,  XIV,  and  XVI.  In  the  present 
chapter  we  are  content  merely  to  point  out  that  the  theories 
of  which  it  treats  are  crude  and  superficial.  They  contain 
a  modicum  of  truth,  but  they  do  not  reach  the  root  causes 
of  interest.  It  is  true  that  explicit  interest  is  dependent 
upon  implicit  interest;  but  this  being  so,  the  question 
still  remains.  What  determines  implicit  interest?  Again, 
it  is  true  that  the  rate  of  interest,  like  every  other  ratio  of 
exchange,  depends  on  "supply  and  demand";  but  the 
question  is.  What  constitutes  the  supply  and  demand? 
And  again,  it  is  true  that  interest  varies  with  loanable  funds ; 
but  what  causes  the  variation  of  those  funds?  To  answer 
these  ulterior  questions,  more  careful  and  elaborate  theories 
have  been  constructed.  These  will  be  considered  in  the 
three  following  chapters. 


CHAPTER  II 

PRODUCTIVITY   THEORIES 
§1 

In  the  previous  chapter  it  was  shown  that  the  problem 
of  interest  is  not  confined  to  contract  or  explicit  interest,  but 
includes  the  much  broader  field  of  natural  or  implicit 
interest.  The  existence  of  implicit  as  distinct  from  ex- 
plicit interest  needs  emphasis,  for  the  reason  that,  to  most 
persons,  the  "rate  of  interest"  means  simply  the  explicit 
rate  of  interest  in  a  loan  contract.  Wlien  a  personal  note, 
mortgage,  or  corporation  bond  is  issued,  the  "rate  of  in- 
terest" is  explicitly  named  in  it  and  agi'eed  upon  by  the 
contracting  parties.  But  after  its  issue  and  before  matur- 
ity, this  note  or  bond  may  change  hands ;  and  as  the  price 
of  sale  is  seldom  exactly  par,  the  investor  evidently  "real- 
izes" a  "rate  of  interest"  on  his  investment  different  from 
the  rate  named  in  the  wi'itten  instrument.  This  rate  is  not 
explicit,  but  implicit.  It  is  implied  by  the  price  of  the 
note  or  bond,  and  can  be  ascertained  from  bond  tables.^ 
This  implicit  rate  of  interest  is  such  that  when  it  is  used 
for  calculating  the  present  values  of  the  future  payments 
of  the  bond  (the  "principal"  and  "interest"),  the  sum  of 
those  present  values  will  be  the  price  of  the  bond. 

It  is  evident  that  not  bonds  and  notes  alone,  but  all  se- 
curities, imply  in  their  price  and  their  expected  returns  a 
rate  of  interest.  Tliere  is  thus  an  implicit  rate  of  interest 
in  stocks  as  well  as  in  bonds.  In  the  case  of  stocks  the 
element  of  chance  enters  also;  but  while  this  adds  some- 
what to  the  intricacy  of  the  calculation,  it  still  requires  the 

^  See  The  Nature  of  Capital  and  Income,  New  York  (Macmillan), 
1906,  Chap.  XIII. 

10 


Sec.  2]  PRODUCTIVITY  THEORIES  11 

employment  of  a  rate  of  interest/  In  the  same  way  all 
instruments  of  wealth,  such  as  land,  imyly  a  rate  of  interest. 
This  is  recognized  when  land  is  sold  on  the  basis  of  a  num- 
ber of  "years'  purchase."  In  like  manner,  machinery, 
dwellings,  furniture,  and,  in  fact,  all  articles  of  wealth, 
as  was  shown  in  The  Nature  of  Capital  and  Income,  are 
valued  by  discounting  expected  income ;  and  all  discomiting 
of  income  can  be  calculated  only  by  means  of  a  "rate  of 
interest."  There  is  thus  an  "implicit  rate  of  interest"  in 
the  value  of  every  capital-good.  It  is,  to  be  sm-e,  often 
difficult  to  work  out  this  rate  definitely,  on  accoimt  of  the 
elusive  element  of  chance;  but  it  has  an  existence  in  all 
capital.  From  this  it  is  clear  that  the  extent  and  impor- 
tance of  the  interest  problem  cannot  be  grasped  until 
implicit  interest  is  recognized ;  and,  as  a  matter  of  history, 
it  was  only  after  implicit  interest  was  in  some  degree  thus 
recognized  that  any  theory  of  interest  worthy  of  the  name 
was  evolved. 

§2 

The  first  wi'iter  who  attempted  to  explain  natural  or 
implicit  interest,  as  distinct  from  contractual  or  explicit 
interest,  appears  to  have  been  Tm'got.  His  explanation 
consisted  simply  in  shifting  the  onus  of  the  problem  on  to 
land.  He  explained  that  interest  must  be  obtainable  from 
the  use  of  capital  in  general,  because  it  is  obtainable  from 
the  use  of  land  in  particular.  He  reasoned  that,  were  it 
not  likewise  obtainable  from  other  capital,  every  one  would 
invest  in  land.  A  man  with  $1000  worth  of  other  goods 
would,  if  he  received  no  increase,  prefer  to  sell  these  goods 
and  buy  $1000  worth  of  land,  from  which  he  could  obtain 
say  $50  a  year.  Land,  he  explained,  evidently  yields 
interest  because  it  yields  a  perpetual  series  of  crops,  the 
land  being  bought  for  so  many  "years'  purchase"  of  those 
crops.  This  number  of  years'  purchase,  he  said,  was  de- 
'  See  The  Nature  of  Capital  and  Income,  Chap.  XVI. 


12  THE  RATE  OF  INTEREST  [Chap.  II 

termined  by  "supply  and  demand";  but  back  of  this 
convenient  phrase  he  did  not  penetrate. 

Turgot's  shifting  the  problem  to  land  might  naturally 
have  revealed  the  true  theory  of  interest  as  lying  in  the 
preference  for  present  over  future  goods;  for  when  one 
asks  why  land  does  not  have  an  infinite  value,  equal  to  the 
entire  value  of  its  infinite  future  crops,  the  answer  becomes 
at  once  obvious,  namely,  that  no  one  would  prize  crops  to 
accrue  a  million  years  hence  on  an  equal  footing  with  crops 
of  to-day.     Yet  this  explanation  was  never  made. 

Turgot's  theory  may  be  regarded  as  a  particular  species 
of  the  numerous  productivity  theories,  differing  from  the 
others  chiefly  in  that  he  took  his  starting-point  from  the 
productivity  of  a  particular  form  of  capital,  instead  of 
from  the  productivity  of  capital  in  general.  At  the  basis 
of  all  the  thought  of  Turgot,  as  of  other  physiocrats,  is  the 
idea  that  land  is  the  source  of  all  human  revenue. 


§3 

This  idea  few  share  to-day;  yet  there  are  many  who, 
consciously  or  unconsciously,  ascribe  the  phenomena  of 
interest  to  the  productivity  of  capital  in  general.  When 
the  rate  of  interest  is  5  per  cent.,  nothing  at  first  sight 
seems  more  obvious  than  that  this  is  so  because  capital 
will  yield  5  per  cent.  Since  capital  is  productive,  it 
seems  self-evident  that  an  investment  of  $100  in  produc- 
tive land,  machinery,  or  any  other  form  of  capital  will 
receive  a  rate  of  interest  proportionate  to  its  productivity. 
Yet  a  very  slight  examination  will  suffice  to  show  the  in- 
adequacy of  this  explanation. 

The  productivity  theory  in  its  simplest  or  "naive"  form, 
as  Bohm-Bawerk  calls  it,  confuses  what  we  have  distin- 
guished ^  as  physical-productivity  and  value-return.  It 
takes  no  account  of  the  great  gap  between  the  physical- 

*  See  The  Nature  of  Capital  and  Income,  Chap.  XI. 


Sec.  3]  PRODUCTIVITY  THEORIES  13 

productivity  of  a  factory  —  the  ratio  of  its  output  to  the 
size  of  the  plant  —  and  its  value-return  —  the  ratio  of  the 
value  of  the  output  to  the  value  of  the  factory/ 

It  is  evident  that  if  an  orchard  of  ten  acres  yields  100 
barrels  of  apples  a  year,  the  physical-productivity,  ten 
barrels  per  acre,  does  not  of  itself  give  any  clew  to  what  rate 
of  return  on  its  value  the  orchard  yields.  To  obtain  the 
value-return,  we  must  reduce  both  income  and  capital  to 
a  common  standard  of  value.  If  the  net  annual  crop  of 
apples  is  worth  $1000  and  the  orchard  is  worth  $20,000, 
the  ratio  of  the  former  to  the  latter,  or  5  per  cent.,  is  a 
rate  of  value-return ;  and  if  this  rate  is  maintained  without 
depreciation  of  the  value  of  the  orchard,  this  rate  of  value- 
return  is  also  the  rate  of  interest. 

It  seems  at  first  sight  very  easy  to  pass  from  quantities 
to  values,  —  to  translate  the  ten  acres  of  orchard  and  the 
100  barrels  of  apples  into  dollars.  But  this  apparently 
simple  step  begs  the  whole  question.  The  important  fact, 
and  the  one  lost  sight  of  in  the  productivity  theory,  is  that 
the  value  of  the  orchard  depends  upon  the  value  of  its  crops ; 
and  in  this  dependence  lurks  implicitly  the  rate  of  interest 
itself.  The  statement  that  "capital  produces  income"  is 
true  only  in  the  physical  sense ;  it  is  not  true  in  the  value 
sense.  That  is  to  say,  capital-value  does  not  produce  in- 
come-value. On  the  contrary,  income-value  produces 
capital-value.  It  is  not  because  the  orchard  is  worth 
$20,000  that  the  annual  crop  will  be  worth  $1000,  but  it  is 
because  the  annual  crop  is  worth  $1000  that  the  orchard 
will  be  worth  $20,000.  The  $20,000  is  the  discounted  value 
of  the  expected  income  of  $1000  per  annum;  and  in  the 
process  of  discounting,  a  rate  of  interest  of  5  per  cent,  is 
implied.  In  general,  it  is  not  because  a  man  has  $100 
worth  of  property  that  he  will  get  $5  a  year,  but  it  is  because 

*  Certain  theories,  which  Bohm-Bawerk  calls  "indirect  produc- 
tivity theories,"  have  taken  account  in  some  degree  of  the  distinc- 
tion between  the  relation  of  quantity  and  value  of  income  to  quan- 
tity and  value  of  capital,  and  have  attempted  to  bridge  the  chasms 
between  them,  but,  as  Bohm-Bawerk  has  shown,  without  success. 


14  THE  RATE  OF  INTEREST  [Chap.  II 

he  will  get  that  $5  a  year  that  his  property  is  worth  $100. 
In  short,  when  capital  and  income  are  measured  in  value, 
their  causal  connection  is  the  reverse  of  that  which  holds 
true  when  they  are  measured  in  quantity.  The  orchard 
produces  the  apples ;  but  the  value  of  the  apples  produces 
the  value  of  the  orchard. 

§4 

We  see,  then,  that  present  capital-w;ea/^/i  produces  future 
income-services;  but  future  income-uaZite  produces  present 
capital-vaZw€.  The  order  to  be  observed  in  the  study 
of  capital  and  income  is  consequently  as  follows:  (1) 
quantity  of  capital,  or  capital-wealth,  (2)  quantity  of 
income,  or  income-services,  (3)  value  of  income,  (4)  value 
of  capital.     This  order  is  shown  in  the  f oUowing  scheme :  — 


Quantities 
Values 


Present  Future 

Capital  Income 


Capital-wealth  — >■  Income-services 
Capital-value  -< —  Income-value 


This  scheme  signifies  that  (1)  any  capital-wealth,  such, 
for  instance,  as  land,  railways,  factories,  dwellings,  or  food, 
is  the  means  for  obtaining  income-services,  whether  these 
be  preparatory  services  like  production  of  crops,  trans- 
portation, and  manufactm'ing  transformations,  or  final 
services  like  shelter  and  nourishment.  This  first  step  in 
the  sequence  pertains  to  the  study  of  the  "technique" 
of  production  and  involves  no  rate  of  interest.  (2)  The  in- 
come-services are  next  reduced  to  a  single  denomination, 
such  as  dollars  of  gold.  This  step  pertains  to  the  study  of 
prices,  and,  when  applied  to  the  final  services,  such  as  shel- 
ter and  nourishment,  does  not  directly  involve  any  rate  of 
interest.  (3)  From  the  income-value  thus  obtained  is  com- 
puted the  value  of  the  original  capital  by  the  process  of 


Sec.  5]  PRODUCTIVITY  THEORIES  15 

discounting.  This  final  process  introduces  the  element  of 
interest.  It  is  clearly  with  this  last  process  that  we  are 
concerned  in  the  study  of  interest. 

The  paradox  that,  when  we  come  to  the  value  of  capital, 
it  is  income  which  produces  capital,  and  not  the  reverse, 
is,  then,  the  stumbling-block  of  the  productivity  theorists. 
It  is  clear,  of  course,  in  any  ordinary  investment,  that 
the  selling  value  of  a  stock  or  bond  is  dependent  on  its 
expected  income.  And  yet  business  men,  although  they 
are  constantly  employing  this  discount  process  in  every 
specific  case,  usually  cherish  the  illusion  that  they  do  so 
because  their  money  could  be  ''productively  invested" 
elsewhere.  They  fail  to  observe  that  the  principle  of 
discounting  the  future  is  universal,  and  applies  to  any 
investment  whatsoever,  and  that  in  such  a  discount- 
process  there  is  necessarily  involved  a  rate  of  interest. 
Consequently,  any  attempt  to  deduce  the  rate  of  interest 
from  the  ratio  of  the  income  from  capital  to  the  value  of 
that  capital  is  a  petitio  principii. 


§5 

The  futility  of  the  ordinary  productivity  theory  may  be 
further  illustrated  by  observing  the  effect  of  a  change  of 
productivity.  If  an  orchard  could  in  some  way  be  made 
to  yield  double  its  original  crop,  the  productivity  of  that 
capital  in  the  physical  sense  would  be  doubled,  but  its  yield 
in  the  sense  of  the  rate  of  interest  would  not  necessarily  be 
affected  at  all,  certainly  not  doubled.  For  the  orchard 
whose  yield  of  apples  should  increase  from  $1000  worth  to 
$2000  worth  would  itself  correspondingly  increase  in  value 
from,  say,  $20,000  to  something  like  $40,000,  and  the  ratio 
of  the  income  to  the  capital-value  would  remain  about  as 
before,  namely,  5  per  cent.  To  raise  the  rate  of  interest 
by  raising  the  productivity  of  capital  is,  therefore,  like 
trying  to  raise  one's  seK  by  one's  boot-straps. 


16  THE  RATE  OF  INTEREST  [Chap.  II 

One  cannot  escape  this  conclusion  (as  has  sometimes 
been  attempted)  by  supposing  the  increasing  produc- 
tivity to  be  universal.  It  has  been  asserted,  in  substance, 
that  though  an  increase  in  the  productivity  of  one  orchard 
would  not  appreciably  affect  the  total  productivity  of 
capital,  and  hence  would  not  appreciably  affect  the  rate 
of  interest,  yet  if  the  productivity  of  all  the  capital  of  the 
world  could  be  doubled,  the  rate  of  interest  would  be 
doubled.  It  is  true  that  doubling  the  productivity  of 
the  world's  capital  would  not  be  entirely  without  effect 
upon  the  rate  of  interest ;  but  this  effect  would  not  be  in 
the  simple  direct  ratio  supposed.  Indeed,  an  increase 
of  the  productivity  of  capital  would  probably  result  in  a 
decrease,  instead  of  an  increase,  of  the  rate  of  interest.  To 
double  the  productivity  of  capital  might  more  than  double 
the  value  of  the  capital.  That  it  would  fail  to  do  so  has 
not  been  shown  by  the  productivity  theorists,  much  less 
that  capital  would  remain  unchanged  in  value. 


§6 

The  same  objections  which  have  been  indicated  in 
relation  to  the  productivity  theory  apply  to  what  Bohm- 
Bawerk  calls  the  "use  theories."  Tliese,  in  fact,  are  a 
special  and  improved  form  of  the  productivity  theory.  The 
ordinary  productivity  theory  regards  capital  as  producing 
an  unspecified  something  called  its  "product,"  whereas 
the  use  theory  regards  that  something  specifically  as  a  use 
or  service.  This  accords  to  some  extent  with  a  correct 
theory  of  services,  but  nevertheless  it  is  still  subject  to  the 
objections  which  have  just  been  made  to  the  other  produc- 
tivity theories.  If  a  machine  renders  a  service  or  use  of 
which  the  annual  value  is  reckoned  at  $100,  and  the  life  of 
the  machine  is  ten  years,  this  $1000  of  services  distributed 
over  a  decade  gives,  of  itself,  no  intimation  as  to  the  rate 
of  interest.     Here,  again,  we  must  first  know  the  rate  of 


Sec.  6]  PRODUCTIVITY  THEORIES  17 

interest  itself  in  order  to  know  the  value  of  the  machine. 
Suppose  that  the  rate  of  interest,  on  the  basis  of  which 
the  machine  is  valued,  is  5  per  cent.  Then  the  value  of 
the  machine,  when  new,  would  be  $772,  this  being  the  dis- 
counted value,  at  5  per  cent.,  of  the  income  above  speci- 
fied. This  capital-value  is,  of  course,  derived  from  the 
expected  income,  and  not  vice  versa.  If,  for  any  reason, 
the  services  of  the  machine  are  doubled  in  quantity,  and 
the  price  of  these  services  remains  unchanged,  their  value 
will  rise  and  become  $200  a  year  for  each  of  the  ten  years. 
But  the  effect  will  not  be  to  double  the  rate  of  interest ;  it 
will  rather  be  to  double  the  capital-value  of  the  machine, 
and  instead  of  being  worth  $772,  which  is  the  discounted 
value,  at  5  per  cent.,  of  $100  a  year  for  ten  years,  it  will 
now  be  worth  $1544,  which  is  the  discounted  value,  at  5  per 
cent.,  of  $200  a  year  for  ten  years. 

Actually,  of  course,  the  doubling  of  the  income-services 
performed  by  the  machine  will  lower  the  price  of  those  ser- 
vices and  affect  the  manufacture  of  the  machine  which 
performs  them.  \Vhen  the  effects  are  complete,  the  resultant 
income-value  of  the  services  of  the  machine  may  rise  above, 
fall  short  of,  or  remain  stationary  at  $200  a  year,  according 
to  the  extent  of  the  fall  in  the  price  of  the  services.  As  a 
consequence  of  such  a  changed  income-value,  the  capital- 
value  of  the  machine  may  also  change  in  either  direction,  or 
remain  stationary.  The  capital-value  follows  the  rate  of 
interest,  not  the  reverse.  Whatever  the  effect  on  the  rate  of 
interest  involved  in  these  events,  it  is  not  the  simple  one, 
imagined  by  the  use  theorists,  of  a  rise  or  fall  proportionate 
to  a  rise  or  fall  in  income-services,  or  even  to  a  rise  or  fall 
of  income-value. 

Tlie  objections  which  have  been  urged  to  the  produc- 
tivity and  use  theories  apply  with  still  greater  force  in  cases 
where  the  depreciation  of  capital  is  offset  so  as  to  "  stand- 
ardize" ^  the  income.  It  is  sometimes  said  that  interest 
is  the  income  which  capital  yields  beyond  what  is  neces- 
*  See  The  Nature  of  Capital  and  Income,  Chap.  XIV. 


18  THE  RATE  OF  INTEREST  [Chap.  II 

sary  to  replace  the  capital.  But  in  the  cost  of  replacement 
which  maintains  the  capital  there  lurks  again  the  very 
rate  of  interest  to  be  explained. 

Let  us  examine  the  case  of  a  factory  plant  of  ten  machines, 
each  like  the  one  just  described.  Suppose  that  these  ten 
machines  are  evenly  distributed  through  the  years,  as  to 
wear  —  that,  for  instance,  the  life  of  each  machine  is  ten 
years  and  that,  accordingly,  the  cost  of  renewal  is  the  cost 
of  one  machine  annually.  Let  us  imagine  a  man  buying 
these  ten  machines  for  $4556.  Knowing  that  the  cost  of 
each  machine  is  $772  and  its  annual  use  is  $100,  he  will 
calculate  that  he  is  ''making  5  per  cent,  on  his  capital," 
because  he  will  receive  10  x  $100  or  $1000  a  year  in  service 
from  his  machines,  and  will  spend  each  year  for  replace- 
ment $772.  This  leaves  a  net  income  of  $228,  which, 
divided  by  the  capital  invested,  $4556,  makes  just  5  per 
cent.  If  asked  why  the  rate  of  interest  is  5  per  cent.,  this 
owner  is  likely  to  answer,  because  outfits  like  his  yield 
5  per  cent,  on  their  cost,  over  and  above  the  cost  of  replace- 
ment. A  little  reflection,  however,  will  show  that  the  rate 
of  interest  is  implicitly  assumed  in  his  calculation.  Not 
only  the  $4556  of  capital,  hut  even  the  $228  of  income,  are 
calculated  on  the  assumption  of  a  rate  of  interest  of  5 
per  cent. 

That  this  is  true  of  the  capital,  $4556,  is  evident  by  re- 
peating, with  reference  to  the  entire  ten  machines,  the 
calculations  already  explained  for  one.  Each  machine  is 
valued  by  discounting  its  future  annual  services  of  $100  for 
its  lifetime.  One  of  the  machines  is  new  and  has  a  life 
of  ten  years;  consequently,  it  is  worth,  as  already  seen, 
$772,  this  being  the  discounted  value  of  ten  annual  instal- 
ments of  $100  each,  on  the  assumption  of  a  5  per  cent, 
interest  rate  as  the  basis  for  the  calculation.  The  life  of  the 
next  machine  is  only  nine  years,  making,  by  a  similar  reck- 
oning, a  present  value  of  $711 ;  the  hfe  of  the  third  machine, 
eight  years,  making  its  value  $646,  and  so  on.  Tlius  the 
total  for  the  ten  machines  is  $772  +  $711  +  $646  +  $578 


Sec.  6]  PRODUCTIVITY  THEORIES  19 

+  $508  +  $433  +  $355  +  $272  +  $186  +  $95,  or  $4556.  It 
is  clear  that  this  item  and  each  of  the  ten  sums  of  which  it 
is  composed  are  calculated  only  by  the  aid  of  a  rate  of  interest. 

So  much  for  the  capital;  now  let  us  turn  to  the  net  in- 
come of  $228.  The  gross  income  is  $100  per  machine  for 
ten  machines,  or  $1000,  and  from  this  is  deducted  the  cost 
of  replenishing  one  machine.  This  cost  is  $772,  leaving 
$228  as  net  income.  But  this  cost  of  replacement,  $772,  is 
the  capital-value  of  a  machine,  and  is  obtained  by  means 
of  a  rate  of  interest,  namely,  5  per  cent.  The  reason,  then, 
that  the  $4556  yields  $228,  or  5  per  cent.,  is  not  because  of 
the  productivity  of  the  machines,  but  because  5  per  cent. 
is  assumed  in  the  calculation  both  of  the  $4556  and  of  the 
$228.  The  5  per  cent,  emerges  at  the  end  only  because  it 
was  put  in  at  the  beginning.^ 

Were  the  productivity  the  source  of  the  rate  of  interest, 
we  should  expect  a  double  productivity  to  double  the  rate 
of  interest.  But  the  reasoning  used  in  the  case  of  the  or- 
chard shows  that  not  only  will  the  value  of  the  use  of  the 
machinery  be  doubled,  but  the  cost  of  each  new  machine 
may  be  doubled,  so  as  to  leave  the  rate  of  interest  at 
5  per  cent. 

As  stated  above,  the  doul^ling  in  productivity  would 
naturally  result  in  lowering  the  price  of  the  services  pro- 
duced, so  that  the  valiie  of  the  doubled  quantity  of  ser- 
vices might  be  less  than  double  the  value  of  the  original 
quantity  of  services.  Consequently,  the  value  of  the  new 
machines  and  the  cost  of  replacing  an  old  machine  by 
a  new  one  might  not  be  double  what  they  were  before. 
But  they  certainly  would  not  be  unaffected. 

The  process  of  adjusting  supply  and  price  reconciles 
what  has  been  said  with  the  old  cost-of-production  theory 
of  value.  The  reader  may  have  felt  that  we  have  treated 
the  value  of  the  machines  and  the  cost  of  replacement  as 
though  they  had  no  relation  whatever  to  the  cost  of  pro- 
ducing the  machines.     One  cannot  deny  that  the  classical 

*  For  a  mathematical  formulation,  see  Appendix  to  Chap.  II,  §  1. 


20  THE  RATE  OF  INTEREST  [Chap.  II 

economists  were  partly  right  in  ascribing  value  to  cost  of 
production.  But  cost  of  production  affects  the  value  of 
a  capital  good  only  indirectly  by  affecting  the  scarcity  of 
its  products  or  uses.  The  value  of  its  products  or  uses 
depends  on  its  marginal  utility.  The  marginal  utility  is 
dependent  on  the  scarcity,  and  this  scarcity  depends,  in 
turn,  partly  on  cost  of  production,  so  far  as  this  cost 
of  production  has  any  independent  existence.^ 


§  7 

Extreme  cases  are  always  instructive,  even  when  they  are 
impossible  of  realization.  As  an  extreme  case,  let  us  im- 
agine a  community  in  which  the  rate  of  interest  is  zero. 
In  this  case  we  can  scarcely  fail  to  observe  the  wide  dif- 
ference between  physical-productivity  and  value-return; 
for  we  shall  find  that  the  disappearance  of  interest  does 
not  carry  with  it  the  disappearance  of  physical-produc- 
tivity, though  it  does  bring  about  the  cessation  of  value- 
return.  Consider  a  plant  of  ten  machines,  of  which  the 
annual  use  is  worth,  as  before,  $100.  The  value  of  a  new 
machine  to  last  ten  years  will  now  be,  not  $772  as  before, 
but  $1000,  this  being  the  capital-value  of  ten  annual  in- 
stalments of  $100  each,  reckoned  at  full  value,  or,  if  we 
prefer  to  say  so,  each  discounted  at  zero  per  cent.  Simi- 
larly, the  value  of  a  machine  one  year  old,  having  nine  more 
years  of  life,  would  be,  not  $711  as  before,  but  $900;  of 
one  two  years  old,  $800,  and  so  on,  making  a  total  value,  not 
of  $4556,  but  $1000  +  $900  +  $800  +  $700  +  $600 -F  $500 
+  $400  +  $300  +  $200  +  $100,  or  $5500.  This  is  the  capi- 
tal-value of  the  plant.  We  next  seek  the  net  annual  income 
from  the  ten  machines.  Strange  as  it  may  seem,  this 
net  income,  if  the  plant  is  exactly  kept  up,  would  be  zero ; 
for  the  gross  annual  income  from  the  ten  machines  is 
10  X  $100,  or  $1000,  and  the  deduction  for  the  cost  of  a  new 

*  See  The  Nature  of  Capital  and  Income,  p.  173. 


Sec.  7]  PRODUCTIVITY  THEORIES  21 

machine  is,  as  we  have  seen,  also  $1000.    Consequently 

the  net  income  is  zero,  and  the  value-return,  being  _..^ , 

5500 

is  also  zero.     Yet  the  case  supposed  does  not  imply  any 

reduction  in  physical-productivity;   the  machines  produce 

the  same  amount  of  work  as  when  the  rate  of  interest  was 

supposed  to  be  5  per  cent. 

It  may  be  asked  how  it  is  possible  that  the  plant,  if  it 
yields  no  income,  could  have  any  value.  We  have  found  it 
worth  $5500  and  yet  it  yields  no  net  income.  The  answer 
is  that  the  annihilation  of  net  income  which  we  have  wit- 
nessed takes  place  only  so  long  as  the  up-keep  of  the  plant 
is  maintained.  At  any  time  that  the  owner  of  the  plant 
sees  fit  to  do  so,  he  may  draw  income  from  the  plant  to 
any  amount  up  to  $5500,  but  no  more.  If,  for  instance,  he 
decides  at  the  end  of  ten  years  to  withdraw  from  manu- 
facturing, he  may  discontinue  his  annual  renewals  and  ob- 
tain in  the  first  year  thereafter  his  $100  income  from  each 
of  the  ten  machines,  or  $1000  in  all,  without  any  deduc- 
tion for  up-keep.  During  the  next  year,  as  one  machine 
will  have  been  worn  out  and  unreplaced,  he  will  obtain 
the  income  from  only  nine  machines,  or  $900,  and  likewise, 
in  the  years  succeeding  this,  he  will  obtain  $700,  $600,  etc., 
until  the  last  machine  is  worn  out  and  no  capital  remains. 
The  total  of  this  income  is  evidently  $5500. 

In  other  words  the  owner  of  the  machines,  as  long  as 
he  keeps  up  his  capital,  obtains  no  net  income,  but  he 
has  the  possibility  at  any  time  of  obtaining  a  total  net 
income  of  $5500  simply  by  letting  his  plant  run  down. 
The  possibility  of  obtaining  this  return  keeps  the  value  of 
the  capital  at  $5500  as  long  as  it  is  kept  up.  His  capital  is 
like  a  fixed  treasure  and  remains  $5500.*  The  process  of 
keeping  up  the  capital  is  virtually  to  keep  the  $5500  in 
cold  storage,  so  to  speak. 

*■  For  a  mathematical  treatment  of  this  peculiar  case,  see  Appendix 
to  Chap.  II,  §  2. 


22  THE  RATE  OF  INTEREST  [Chap.  II 

If  it  be  asked  what  motive  could  ever  prompt  any  one 
to  keep  up  his  capital  when,  as  long  as  he  does  so,  all 
income  is  foregone,  the  answer  is  that,  under  our  assump- 
tion of  zero  interest,  there  would  be  no  preference  for  the 
immediate  over  the  remote  income  of  $5500.  The  owner 
of  the  plant  would  just  as  willingly  wait  a  hundred  years 
for  his  $5500  as  to  receive  it  now.  In  actual  fact,  men  are 
not  thus  willing  to  wait,  and  therein  lies  the  unreality  of 
our  assumption  that  interest  is  zero.  In  our  supposititious 
case  the  element  of  time-preference  was  abstracted  with 
the  element  of  interest.  But  this  imaginary  case  shows 
that  absence  of  interest  is  quite  compatible  with  the  pres- 
ence of  physical-productivity,  and  that,  therefore,  whatever 
element  is  responsible  for  the  existence  of  interest  in  the 
actual  world,  that  element  cannot  be  physical-productivity. 


§  8 

It  was  with  a  view  to  meeting  some  of  the  difficulties 
which  have  just  been  pointed  out  in  the  productivity  theo- 
ries, that  Alexander  Del  Mar  and  Henry  George  suggested 
their  theory  of  interest,^  basing  it  on  the  productivity  of 
those  particular  kinds  of  capital  which  reproduce  them- 
selves. They  state  that,  were  all  capital  inanimate,  the 
phenomena  of  interest  would  not  exist,  because  inanimate 
capital  is  incapable  of  increasing;  but  that  the  organic 
forms  of  capital  are  capable,  without  labor,  of  reproducing 
and  increasing  with  time.  Money,  as  Aristotle  said,  is 
barren,  and  coal  and  iron  cannot  breed.  Were  all  capital 
of  this  non-increasing  kind,  it  would,  said  Henry  George, 
not  yield  interest.  But  a  flock  of  sheep,  herd  of  cattle,  or 
group  of  Belgian  hares  will,  from  its  own  natural  powers 
of  breeding,  increase  and  multiply;   it  will,  as  it  were,  ac- 

»  Del  Mar,  Science  of  Money,  (Macmillan)  1896,  p.  144.  Henry 
George,  Progress  and  Poverty.  For  a  general  criticism  of  this  theory, 
see  D wight  M.  Lowry,  "The  Basis  of  Interest,"  American  Academy 
of  Political  and  Social  Science,  March,  1892,  pp.  53-76. 


Sec.  9]  PRODUCTIVITY  THEORIES  23 

cumulate  at  compound  interest.  In  like  manner  a  forest 
will  grow,  and  crops  will  spring  up.  These  seem  to  show  a 
rate  of  interest  in  Nature  herself.  Mr.  George  contends 
that  a  man  who  puts  SIOOO  into  a  savings  bank  can  de- 
mand that  it  receive  interest,  for  the  reason  that  he  might 
invest  it  in  a  flock  of  sheep  and  let  it  accumulate  naturally. 
According  to  this  theory,  interest  exists  because  plants  and 
animals  grow,  because  the  seed  becomes  the  crop,  the  sap- 
ling becomes  a  tree,  the  egg  a  chick,  and  the  chick  a  hen. 
The  conclusion  is  drawn  that,  in  the  last  analysis,  the  rate 
of  interest  consists  in  the  ''average  rate  of  growth  of  ani- 
mals and  plants." 

We  may  remark  at  the  outset  that  this  theory,  like  the 
land-yielding  theory  of  Turgot,  is  one-sided  and  partial, 
inasmuch  as  it  makes  the  rate  of  interest  from  all  capital 
depend  on  the  rate  of  interest  from  one  particular  form  of 
capital ;  and  it  does  not  seem  likely,  a  jyriori,  that  any  theory 
of  interest  can  be  true  which  does  not  apply  alike  to  all 
forms  of  capital  which  yield  interest.  But,  aside  from 
this  preliminary  objection,  a  specific  examination  of  his 
theory  will  show  that  Henry  George  has  not  escaped  the 
fatal  error  of  assuming  a  rate  of  interest  in  order  to  prove 
it.  We  propose  to  make  a  thorough  reexamination  of  this 
theory,  not  because  it  has  attracted  any  special  attention 
or  been  accepted  by  others  than  its  author  or  authors,  but 
because  it  puts  the  productivity  theory  on  its  strongest 
grounds  —  stronger  grounds  than  its  opponents  have 
usually  acknowledged  or  understood  —  and  more  especially 
because,  in  a  dormant  state,  it  seems  to  exist  in  the  minds 
of  a  great  many  persons. 


§9 

Let  us  imagine  a  forest  growing  at  a  certain  rate,  such,  for 
instance,  that  an  acre  of  spruce  containing  100  cords  of  wood 
suitable  for  making  wood  pulp  will,  if  let  alone,  in  five 


24  THE  RATE  OF  INTEREST  [Chap.  II 

years  amount  to  200  cords.  Here  is  an  increase  of  100 
per  cent,  in  five  years,  which  is  at  the  rate  of  about  15 
per  cent,  per  annum.  Does  this  15  per  cent,  represent  a 
natural  rate  of  interest  ?  Would  100  cords  of  this  year's 
timber  exchange  for  115  cords  of  next  year's  timber?  If 
so,  we  certainly  have  a  simple  physical  basis  for  the  rate 
of  interest  quite  independent  of  the  psychological  element. 
But  a  little  consideration  will  show  that  there  is  an  error 
in  the  reasoning.  If  the  supply  of  wood  pulp  is  decreas- 
ing as  years  go  on,  while  the  demand  is  steadily  increasing 
(and  these  conditions  correspond  to  the  facts  as  they  are 
to-day),  it  may  well  be  that  100  cords  of  this  year's  timber 
would  exchange  for  a  relatively  small  amount  of  next  year's 
timber,  say  105  cords,  in  spite  of  the  fact  that  it  grows 
at  15  per  cent,  per  annum  instead  of  5  per  cent.  That  this 
rate  of  exchange  of  present  wood  for  future  wood  is  quite 
compatible  with  a  much  greater  rate  of  growth  will  be- 
come apparent  as  soon  as  we  consider  that  growing  timber 
is  not  the  same  thing  as  cut  wood.  It  is  clear  that  to 
cut  young  timber  which  is  growing  very  fast  is  like  killing 
the  goose  that  lays  the  golden  egg,  and  to  reckon  the  value 
of  the  growing  timber  as  only  equivalent  to  the  wood 
contained  in  it  is  like  reckoning  a  live  goose  equivalent 
to  a  dead  one.  The  value,  in  cut  wood,  of  100  cords  of 
rapidly  gi'owing  timber  will  be  considerably  greater  than  100 
cords  of  cut  wood.  If,  for  instance,  the  possessor  of  the 
growing  timber  has  the  option,  besides  that  of  cutting  it, 
of  allowing  it  to  stand  for  five  years  and  then  obtaining  a 
stumpage  of  200  cords,  he  will  allow  it  to  stand,  for  these 
200  cords  due  five  years  hence  are  worth,  in  present  esti- 
mation, discounted  at  5  per  cent.,  157  cords.  Thus  his  present 
100  cords  of  standing  timber  is  equivalent  to  157  cords  of 
present  cut  wood.  The  value  of  a  tree  at  any  time  is 
therefore  not  necessarily  the  physical  amount  of  wood 
then  in  it ;  it  may  be  the  discounted  value  of  the  future  wood 
which  the  tree  will  produce  if  left  to  grow.  It  will  actually 
be  whichever  of  the  two  happens  to  be  the  greater.     For, 


Sec.  9] 


PRODUCTIVITY  THEORIES 


25 


of  various  optional  employments  of  his  'capital,  the  investor 
selects  the  one  which  offers  the  maximum  present  value/ 
Were  it  true  that  the  value  of  a  tree  in  wood  were  always 
simply  the  physical  amount  of  wood  it  contains,  it  would 
be  a  matter  of  indifference  whether  a  tree  were  cut  at 
the  sapling  stage  or  any  other,  whereas  we  know  that 
part  of  the  art  of  lumbering  consists  in  selecting  the  right 
age  for  cutting. 
The  case  may  be  illustrated  by  Figure  1.    Let  AB  repre- 


sent the  number  of  cords  of  wood  on  an  acre  of  growing 
trees,  A'B'  the  amount  of  wood  which  may  be  expected 
at  the  end  of  five  years,  A"B"  what  may  be  expected  in 
ten  years,  and  so  on  for  successive  years  until  the  forest 
reaches  its  maximum  growth,  MA'',  at  the  end  of  AM 

*  See  The  Nature  of  Capital  and  Income,  pp.  221-222. 


26  THE  RATE  OF  INTEREST  [Chap.  II 

years,  Tlie  percentage-slope  ^  of  the  curve  BN  at  any 
point,  therefore,  represents  the  rate  of  growth  of  the 
forest.  The  value  at  present  of  the  forest  in  terms  of  cords 
of  wood  will  be  represented,  not  by  the  height  AB,  but  in 
a  different  manner,  as  follows :  If  from  B'  the  discount 
curve  ^  B^C  be  drawn,  the  ordinates  of  which  will  represent 
the  discounted  values  of  A'B'  at  any  times,  AC  will  repre- 
sent the  present  value  of  A'B',  the  wood  if  cut  in  five  years. 
Similarly,  AC"  will  represent  the  present  value  of  A"B", 
the  wood  if  cut  in  ten  years.  Draw  in  like  manner  a  num- 
ber of  discount  curves  until  one  is  found,  tT,  which  is  tan- 
gent to  the  curve  BN.  At  will  then  be  the  correct  value 
of  the  yoimg  forest,  and  D  will  represent  the  time  at  which 
it  should  be  cut.  Clearly,  At  is  quite  different  from  AB, 
the  amount  of  wood  at  the  present  time,  and  also  from 
DT,  the  amount  of  wood  at  the  time  of  cutting.  At  is  the 
maximum  present  value  out  of  all  possible  choices.  If 
the  forest  is  for  some  reason  to  be  cut  at  once,  its  value 
will  be  only  AB;  if  it  is  to  be  cut  at  A',  its  present  value 
will  be  AC ;  if  at  A",  its  present  value  will  be  AC" ;  if  at 
D,  its  value  will  be  At.  At  is  the  maximum,  for  if  the  for- 
est were  cut  at  any  other  point  on  either  side  of  T  the  dis- 
count curve  passing  through  that  point  would  evidently 
pass  below  tT. 

At  the  time  A,  then,  the  wood  in  the  forest  is  only  AB, 
but,  assuming  proper  foresting,  the  value  of  the  forest  in 
terms  of  wood  is  At;  the  rate  of  growth  of  the  forest  is 
the  percentage-slope  of  BN  at  B,  but  the  rate  of  interest 
is  the  percentage-slope  (the  same  at  all  points)  of  tT.  At 
the  point  of  tangency  alone,  namely,  T,  are  the  rate  of 
growth  and  rate  of  interest  identical,  and  to  that  extent 
there  is  truth  in  the  thesis  that  the  rate  of  interest  is  the 
rate  of  growth.    This  element  of  truth  in    the   organic 

*  By  percentage-slope  is  meant  the  ratio  of  the  slope  to  the  ordi- 
nate. See  The  Nature  of  Capital  and  Income,  Appendix  to  Chap. 
XII,  §  2. 

*  See  The  Nature  of  Capital  and  Income,  Chap.  XIII. 


Sec.  9]  PRODUCTIVITY  THEORIES  27 

productivity  theory  will  be  more  fully  discussed  when 
we  come  to  develop  our  own  theory  of  the  rate  of  in- 
terest. But  that  this  element  of  truth  is  insufficient  to 
afford  a  determination  of  the  rate^  of  interest  is  evident 
when  we  consider  that  the  point  at  which  the  forest  is  to 
be  cut  itself  depends,  among  other  causes,  upon  the  rate  of 
interest.  If  the  interest  rate  rises,  the  discount  curves  em- 
ployed become  steeper  and  the  point  of  tangency  T  moves 
toward  the  left ;  that  is,  the  forest  will  be  cut  earlier.  This 
is  undoubtedly  one  reason  for  the  fact  that  forests  in  the 
United  States  have  hitherto  been  cut  early  ;  the  owners 
have  not  felt  that  they  could  afford  to  "lose  the  interest" 
in  waiting.  In  Europe,  on  the  other  hand,  where  interest 
rates  have  been  low,  forestry  culture,  though  often  involv- 
ing fifty  years'  waiting,  has  been  profitable.  It  would 
not  be  correct,  of  course,  to  ascribe  the  difference  in  forest 
policy  wholly  to  a  difference  in  the  rate  of  interest,  for 
the  European  policy  has  also  been  more  enlightened  than 
the  American. 

Not  only  does  the  most  favorable  time  for  cuttmg  depend 
upon  the  rate  of  interest,  but  the  rate  of  interest  itself 
depends  upon  the  future  distribution  of  the  times  of  cut- 
ting of  many  forests.  If  all  the  forests  of  a  country  are 
young,  there  will  be  a  relative  scarcity  of  present  wood  and 
a  consequent  enhancement  of  the  rate  of  interest  (in  terms 
of  wood)  which  will  make  for  early  cutting.  In  the  United 
States  at  the  present  time  the  reverse  is  the  case.  There 
is  a  present  abundant  supply  of  spruce  for  wood  pulp. 
But  a  single  edition  of  a  large  metropolitan  Smiday  news- 
paper will  use  up  two  acres  of  spruce.  We  have,  therefore, 
to  contemplate  a  growing  scarcity  of  wood,  and  probably 
at  the  same  time  an  increasing  demand  for  it.  The  effect 
is  to  enhance  the  value  relatively  of  future  wood,  that  is, 
to  lower  the  rate  of  interest  in  wood.  This  shifts  the  point 
of  tangency  T  toward  the  right  and  introduces  a  ten- 
dency to  postpone  cutting,  as  is  manifested  by  speculation 
in  spruce  forests. 


28  THE  RATE  OF  INTEREST  [Chap.  II 

§  10 

From  what  has  been  said  it  is  clear  that  although  interest 
enters  into  the  processes  of  nature,  it  is  not  because  of  their 
physical  expansion,  but  because  they  require  time.  It  is 
not  because  the  seed  grows  into  crops  or  the  egg  into  a 
chick  that  there  is  interest,  but  because  the  crops  or  the 
chick  are  unavailable  until  a  future  time.  The  type  of 
interest  is  a  "time-lock"  like  those  used  on  the  doors  of 
some  banks.  Nature  holds  many  treasures  in  her  store- 
house, but  she  will  not  unlock  them  all  at  once. 

The  conclusion,  therefore,  from  our  study  of  the  various 
forms  of  the  productivity  theory  is  that  physical-pro- 
ductivity, of  itself,  has  no  such  direct  relation  to  the  rate 
of  interest  as  is  usually  ascribed  to  it;  and  in  the  theories 
which  we  have  examined,  the  rate  of  interest  is  always 
surreptitiously  introduced.  It  is,  however,  quite  true  that 
the  productivity  of  capital  does  ajfect  the  rate  of  interest; 
for  it  affects  the  relative  valuation  of  present  and  future 
goods  by  affecting  the  relative  endowment  of  the  present 
and  the  future.  It  is  quite  true,  in  particular,  that  the 
rapidity  of  growth  of  the  organic  world  will  affect  the  rate 
of  interest  by  redistributing  income  between  different  points 
of  time  and  by  opening  up  a  series  of  choices  to  the  owner 
as  to  the  time  of  cutting  his  forests  or  of  reaping  the 
rewards  of  other  sorts  of  organic  growth.  It  follows  that 
the  rate  of  growth  will  coincide  at  certain  points  with  the 
rate  of  interest.  These  small  grains  of  truth  in  the  pro- 
ductivity theories  will  be  fully  incorporated  in  our  study 
at  a  later  stage. 


CHAPTER  III 

COST   THEORIES 
§    1 

We  turn  now  from  those  theories  of  interest  based  mainly 
on  the  idea  of  -productivity  to  those  based  mainly  on  that  of 
cost. 

The  first  of  the  cost  theories  to  be  examined  resembles 
closely  the  productivity  theories,  the  only  difference  being 
that  the  "cost  of  production  of  capital"  takes  the  place  of 
the  value  of  capital.  In  the  productivity  theories,  the  rate 
of  interest  was  sought  in  the  ratio  between  the  income 
from  capital  and  the  value  of  that  capital.  In  the  cost 
theory  now  considered,  on  the  other  hand,  the  rate  of  in- 
terest is  sought  in  the  ratio  between  the  income  from  capi- 
tal and  the  cost  of  that  capital.  This  theory  is  subject  to 
many  of  the  objections  which  apply  to  the  productivity 
theories.  In  the  first  place,  it  is  necessary,  before  the 
ratio  of  income  to  cost  can  be  regarded  as  even  commen- 
surable with  a  rate  of  interest,  that  income  and  cost  shall 
have  been  reduced  to  a  common  denomination  of  value, 
as,  for  instance,  dollars.  A  loom  renders  its  return,  or  ser- 
vice, by  the  operation  called  weaving.  The  cost  of  the 
loom,  on  the  other  hand,  consists  of  raw  materials,  the  use 
of  tools,  dies,  lathes,  and  other  machine-shop  appliances, 
together  with  human  labor.  Only  when  these  miscella- 
neous items  are  reduced  to  some  common  standard  of  value 
does  the  ratio  of  income  to  cost  become  a  mere  percentage 
like  the  rate  of  interest.  But  when  this  reduction  to  a 
common  standard  is  effected,  the  suspicion  immediately 
arises  that,  after  all,  the  question  of  interest  may  have 

29 


30  THE  RATE  OF  INTEREST  [Chap.  Ill 

been  begged  in  the  process,  —  that  the  labor,  materials, 
and  use  of  tools  all  derive  their  value  as  costs,  in  part,  at 
least,  from  discounting  the  prospective  product  to  which 
they  contribute.  In  other  words,  since  the  cost  of  capi- 
tal must  be  obtained  by  a  process  of  valuation,  this  valua- 
tion may  involve  the  very  rate  of  interest  to  be  determined. 

Nevertheless,  the  theory  which  seeks  the  rate  of  interest 
in  the  ratio  of  return  to  cost  of  capital  has  certain  advan- 
tages over  that  which  seeks  it  in  the  ratio  of  return  to  value 
of  capital;   for  there  are  some  costs  which  are  not  merely 
the   discounted   value   of  expected  services.    There  are 
two    kinds   of   costs,    (1)  "interactions"^   and   (2)  labor- 
and- trouble.      The   value   of    the   former   is   always   de- 
termined  by  discounting  some  future  service;   the  value 
of  the  latter  is  determined  (to  the  laborer)  by  the  irksome- 
ness  or  "undesirabihty"  of  labor  compared  with  the  de- 
sirability of  money.    We  are  not  called  upon,  however, 
to  strengthen  the  cost  theories  by  recourse  to  this  distinc- 
tion between  costs  which  involve  discounting  and  costs 
which  do  not;  for  the  cost  theories  as  actually  held  and 
advocated  take  no  account  of  such  a  distinction,  and  the 
costs  usually   cited   are   mainly  costs  which   do  involve 
discounting,  —  in   other  words,  interactions.     Such    costs 
certainly  cannot  be  taken  as  a  sufficient  foundation  for 
explaining  the  rate  of  interest.    The  tailor  reckons  among 
his  costs  the  value  of  the  cloth  which  he  buys ;   the  manu- 
facturer of  the  cloth  reckons  among  his  costs  the  value  of 
the  yarn ;   the  producer  of  the  yam  reckons  in  his  cost  the 
value  of  the  wool.     But  the  value  of  the  wool  is  found  in 
part  by  discountmg  the  value  of  the  yarn  to  which  it 
contributes;    that  of  the  yarn,  by  discounting  the  value 
of  the  cloth;    that  of  the  cloth,  by  discounting  the  value 
of  the  clothes. 

It  is  seldom  possible  in  practice  to  find  a  case  so  pure 
as  not  to  be  obscured  by  a  number  of  different  ele- 
ments;   but   let  us,  for  the  sake  of  illustration,  consider 

1  See  The  Nature  of  Capital  and  Income,  Chaps.  VII-X. 


Sec.  2]  COST  THEORIES  31 

a  dealer  in  trees,  who  buys  saplings  and  sells  them  after 
they  are  full  grown.  In  this  case  there  are  few  other 
costs  besides  the  cost  of  buying  the  saplings.  We  can  here 
see  clearly  the  fallacy  involved  in  regarding  the  rate  of  in- 
terest as  determined  by  the  ratio  of  the  value  of  the  full- 
grown  tree  to  the  cost  of  the  sapling ;  for  the  cost  of  buying 
the  sapling  is  evidently  itself  obtained  by  discounting  the 
value  of  the  tree.  In  fact,  in  this  case  the  cost  theory 
becomes  identical  with  the  productivity  theory;  for  the 
cost  of  buying  the  sapling  is  nothing  more  nor  less  than  the 
value  of  the  sapling.  The  only  distinction  between  them 
is  a  formal  one :  the  cost  of  buying  the  sapling  is  regarded 
as  pertaining  to  the  income  and  outgo  account;  the  value 
of  the  sapling,  to  the  capital  account.  Since,  then,  the 
cost  of  buying  the  sapling  is  the  discounted  value  of  the 
tree,  this  cost  can  be  computed  only  by  discounting,  and 
discounting  presupposes  a  rate  of  interest.  In  many 
cases,  therefore,  "cost"  is  merely  the  discounted  value  of 
"return."  The  cost,  in  these  cases  at  least,  depends  on 
the  rate  of  interest,  not  the  rate  of  interest  on  the  cost. 


§  2 

It  is  true  that  an  article  sometimes  costs  less  (or  more) 
than  the  discounted  value  of  the  returns.  The  ratio  of 
future  return  to  present  cost  may  then  temporarily  differ 
from  the  rate  of  interest  on  loans.  Thus,  a  manufacturer 
calculates  that  a  newly  invented  machine  will  earn  him 
$10  a  year  for  twenty  years.  If  we  suppose  he  is  willing 
to  invest  on  a  5  per  cent,  basis,  namely,  that  subjectively 
he  values  this  year's  goods  at  a  premium  of  5  per  cent, 
compared  with  next  year's  goods,  then  the  price  he  is 
willing  to  pay  for  the  machine  is  $125,  this  being  the 
present  worth,  at  5  per  cent.,  of  $10  a  year  for  twenty  years. 
But  it  may  be  that  the  cost  of  obtaining  the  machine  is 
not  $125  but,  say,  $100,  which  corresponds  to  an  8  per 


32  THE  RATE  OF  INTEREST  [Chap.  Ill 

cent,  basis.  Here  seems  to  be  a  natural  rate  of  interest  of 
8  per  cent.,  in  defiance  of  an  interest  rate  of  5  per  cent,  em- 
ployed by  the  manufactm-er  in  discounting  his  returns. 
The  manufacturer,  by  investing  $100,  makes  8  per  cent.  — 
not,  apparently,  because  he  or  any  one  else  discounts  the 
future  at  that  rate,  but  simply  because  of  the  productivity 
of  the  machine  in  relation  to  its  cost. 

But  such  a  disharmony  between  the  8  per  cent,  realized 
and  the  5  per  cent,  employed  in  discounting  will  be  only  tem- 
porary. It  will  work  out  its  own  correction,  for  the  manu- 
facturer who  finds  he  can  invest  at  8  per  cent,  when  he 
is  willing  to  invest  at  5  per  cent,  will  increase  his  invest- 
ment until  the  returns  fall  to  5  per  cent.  He  will  buy 
more  machines;  but  the  more  he  buys,  the  less  will  he 
make  from  each  successive  machine.  The  tenth  machine 
will  not  increase  his  income  rate  by  $10  over  and  above 
what  it  would  be  with  only  nine  machines,  but  by,  let  us 
say,  only  $6.25.  This  reduction  may  be  due  to  outrun- 
ning his  market  and  reducing  the  price  he  can  get,  or  by 
increasing  the  cost  of  running,  or  in  other  ways.  He  will 
buy  machines  up  to  the  point  where"  the  last  increment 
earns  5  per  cent.,  and  by  the  "law  of  indifference"  he  will 
impute  this  same  rate  to  all  the  machines.  In  other  words, 
however  much  the  ratio  of  return  to  cost  may  temporarily 
deviate  from  the  rate  of  preference  for  present  over  future 
goods,  such  deviation  is  done  away  with  at  the  margin  of 
final  choice.  Excessive  rates  of  return  could  never  serve 
as  a  permanent  basis  for  market  values,  for  the  rush  to 
secure  these  excessive  returns  would  reduce  them.  If,  on 
the  other  hand,  the  cost  of  the  machine  is  $150,  represent- 
ing a  basis  of  about  3  per  cent.,  while  the  manufacturer 
continues  willing  to  invest  only  on  a  5  per  cent,  basis, 
there  may  seem  to  be  a  natural  rate  of  3  per  cent.  Here, 
too,  the  apparent  disharmony  will  work  out  its  own  cor- 
rection. The  manufacturer  will  cease  buying  machines  to 
replace  the  old  ones  which  have  worn  out,  mitil  through 
such  limitation  the  returns  have  increased  to  5  per  cent. 


Sec.  3]  COST  THEORIES  33 

In  either  case,  when  equilibrium  is  estabhshed  the  value  of 
the  machine  is  the  discounted  value  of  its  future  uses. 
For  the  individual  purchaser,  the  cost  of  the  machine 
appears  as  a  fixed  quantity,  and  he  so  adjusts  the  number 
of  machines  that  the  return  of  the  marginal  machine  is 
5  per  cent,  on  this  cost.  For  the  market  as  a  whole,  how- 
ever, the  situation  is  reversed ;  the  price  of  the  machines  is 
determined  by  their  prospective  return. 


§  3 

So  far  as  the  cost  theories  of  interest  relate  to  labor 
cost,  they  are  free  from  the  objection  of  begging  the  ques- 
tion, which  has  just  been  offered  to  the  more  general  cost- 
theory;  and  yet,  the  ratio  of  return  on  labor  to  the  labor 
invested  cannot,  by  itself,  afford  a  sufficient  basis  for  the 
rate  of  interest,  for  the  reason  that  neither  the  return  nor 
the  labor  are  fixed  quantities.  With  an  increase  in  the 
amount  of  capital,  the  return  will  decrease,  and  the  labor 
of  obtaining  it  will  increase.  This,  in  fact,  is  the  well- 
known  "law  of  diminishing  returns." 

To  render  our  reasoning  clear,  we  shall  take  a  classical 
illustration  of  Roscher's.  Let  the  labor  sacrificed  in  produc- 
ing a  fishing  net  be  reckoned  at  100  fish.  This  valuation  of 
labor  by  the  laborer  is  not  quite  like  the  valuation  of  the 
machine.  Instead  of  being  the  value  of  future  income  dis- 
counted, it  is  the  value  of  present  outgo  in  the  form  of 
effort.  We  cannot,  therefore,  maintain  that  in  valuing  the 
net  the  rate  of  interest  is  surreptitiously  introduced.  Our 
objections  are  now  confined  to  the  fact  that  both  the  labor 
of  making  the  net  and  its  return  are  not  fixed  elements  to 
which  the  rate  of  interest  is  adjusted,  but  are  themselves 
adjustable  to  that  rate.  With  the  net,  the  fisherman  is 
enabled  to  catch  30  fish  a  day,  whereas  without  it  he  could 
catch  but  3.  We  may  suppose  that  the  net  will  last  90 
days,  getting  in  all  2700  fish.    This  is  the  return  on  the 

D 


34  THE  RATE  OF  INTEREST  [Chap.  Ill 

labor  invested,  which  has  been  reckoned  at  100  fish.  If 
the  net  requires  care  and  attention,  and  this  be  reckoned 
at  3  fish  a  day,  there  is  still  an  excess  of  30  —  3,  or  27  fish 
a  day  to  be  credited  to  the  net  itself.  For  the  90  days  this 
amounts  to  2430  fish.  Even  if,  for  other  reasons,  we 
make  further  reductions,  the  return  may  still  be  a  very 
large  one  compared  with  the  100  fish  invested,  —  let 
us  say  2000  fish. 

Tlie  question  now  is,  does  the  excess  of  this  return 
over  the  labor  invested  explain  interest?  Certainly  not. 
Granted  that  such  an  extraordinary  return  on  one's  labor 
invested  were  initially  realized,  it  is  evident  that  nets 
paying  so  handsomely  would  be  made  in  large  numbers, 
and  that,  as  their  numbers  were  increased,  the  labor 
and  sacrifice  of  making  each  additional  net  would  in- 
crease, or  else  the  product  obtained  from  each  additional 
net  would  decrease,  or  both.  In  this  way  the  excess 
of  return  over  cost  would  be  doubly  reduced.  Why  should 
not  this  excess  be  reduced  to  zero  ?  Evidently  nothing  in 
the  physical  nature  of  the  net  itself,  or  the  condition  of 
the  fisheries,  or  the  amoimt  of  labor  involved  in  producing 
a  net,  will  suiftce  to  explain  the  point  at  which  the  process 
will  cease  and  nets  no  longer  be  produced.  On  the  con- 
trary, it  is  evident  that  physically  it  would  be  possible  to 
greatly  overproduce  the  nets.  It  is  also  clear  that  the 
fisheries  could  not  continue  to  yield  fish  indefinitely.  The 
result  might  be  that,  as  the  nets  were  increased  in  num- 
ber, the  labor  of  obtaining  materials  and  making  nets 
would  increase  until,  let  us  say,  a  net  would  cost  labor 
reckoned  equivalent  to  1000  fish;  at  the  same  time  the 
yield  of  each  net  might  fall  to,  say,  10  fish  a  day  for  the 
90  days,  or  900  fish  in  all.  Here  would  be  an  invest- 
ment of  1000  for  a  return  of  only  900.  The  reason  that 
this  result  would  not,  intentionally  at  least,  be  reached,  is 
evidently  not  to  be  sought  in  any  physical  facts  as  to 
the  net,  the  fish,  and  the  labor  of  producing  them,  but  in 
the  fact  that  the  net  makers  would  of  their  own  volition 


Sec.  4]  COST  THEORIES  35 

cease  producing  nets  before  such  a  superabundance  was 
put  upon  the  market.  In  fact,  they  would  even  refuse  to 
invest  1000  for  an  equal  return  of  1000.  In  other  words, 
the  production  of  nets  would  proceed  only  up  to  the  point 
where  the  excess  of  return  over  cost  corresponded  to  the 
relative  preference  for  present  over  future  fish.  The  rea- 
son, then,  that  the  product  keeps  above  the  cost  is  simply 
that  those  who  make  nets  decide  to  stop  making  them  at 
a  point  earlier  than  that  of  equality  between  cost  and  re- 
turn, and  their  decisions  so  to  do  are  based  not  on  a 
physical  but  on  a  psychical  fact  —  their  relative  valua- 
tions of  present  sacrifice  and  future  return. 

Leaving  our  special  illustration,  let  us  put  the  matter 
in  general  terms.  It  is  often  stated  by  economists  that 
any  capital  will  be  constructed  only  so  long  as  its  mar- 
ginal utility  is  equal  to  or  greater  than  the  marginal  dis- 
utility or  marginal  cost  of  its  construction.  The  greater 
the  desire  for  its  services  and  the  less  the  cost  of  produc- 
tion, the  more  of  it  will  be  produced  before  its  marginal 
utility  falls  to  the  level  of  its  marginal  cost.  But  the 
proper  statement  would  be,  not  that  the  marginal  utility 
of  the  services  of  a  capital  instrument  tends  to  equal  the 
marginal  cost  of  the  instrument,  but  that  it  tends  to  reach 
a  level  slightly  above  that  cost,  such  that  the  present  or 
discounted  estimate  of  the  marginal  utihty  of  future  ser- 
vices will  equal  marginal  cost. 


§  4 

Sometimes  the  argument  of  the  cost  theorists  takes  a 
slightly  different  form.  It  is  said  that  the  net,  for  instance, 
receives  interest  because  it  "saves  labor."  If  by  "saving 
labor"  is  meant  that  the  net  costs  less  than  it  produces, — 
that  the  labor  of  constructing  and  tending  the  net,  meas- 
ured in  fish,  is  less  than  the  number  of  fish  caught  by  the 
net,  —  the  argument  is  merely  a  repetition,  in  different 


36  THE  RATE  OF  INTEREST  [Chap.  Ill 

words,  of  the  argument  which  has  just  been  stated  and 
criticised,  that  the  net  receives  interest  because  it  produces 
something  over  and  above  its  cost.  If,  on  the  other  hand, 
by  "saving  labor"  is  meant  simply  that  the  net  catches 
more  fish  than  its  owner  could  catch  without  it  (30  fish 
a  day  instead  of  3),  the  argument  is  superficial;  it  leaves 
entirely  out  of  account  the  cost  of  constructing  the  net, 
which  is  evidently  an  essential  factor  in  reckoning  the  rate 
of  return.  For  aught  which  this  statement  of  "labor- 
saving"  contains,  the  net  might  have  cost  or  be  worth 
10,000  fish.  Such  a  net,  though  "saving  labor"  for  90 
days,  would  never  earn  its  original  cost,  and  there  could  be 
no  interest,  in  spite  of  this  "saving  of  labor." 

The  adherents  of  the  labor-saving  theory  of  interest 
may  put  their  case  in  a  third  and  stronger  form.  They 
may  say  (1)  that  the  net  first  costs  labor  to  produce,  (2) 
that  it  afterward  saves  labor  in  operating,  and  (3)  that  the 
labor  subsequently  saved  exceeds  the  labor  originally  ex- 
pended. The  excess  of  the  labor  saved  over  the  labor 
expended,  both  being  measured,  say,  in  fish,  is,  according 
to  their  theory,  the  source  of  interest.  There  is  an  ele- 
ment of  truth  in  the  theory  as  thus  stated,  and  this 
element  will  be  incorporated  into  the  constructive  argu- 
ment in  Chapter  VIII.  But  the  element  of  truth  is  in- 
adequate to  form  a  complete  theory  of  interest  for  the 
reason  that  the  excess  of  labor  saved  over  labor  spent  is 
not  a  fixed  excess,  but  depends  on  the  voluntary  choice  of 
the  fishermen  as  to  the  number  of  nets  they  propose  to 
make.  Their  choice  depends  on  how  much  present  labor 
they  are  willing  to  spend  in  order  to  save  themselves  a 
given  amount  of  future  labor ;  it  depends,  in  other  words, 
on  their  relative  valuation  of  present  and  future  labor. 

§  5 

In  the  example  of  the  net,  labor-sacrifice  and  return  were 
both  measured  in  a   common  objective  standard,  —  fish. 


Sec.  5]  COST  THEORIES  37 

A  still  more  elementary  case  is  that  in  which  both  cost  and 
return  are  measured  in  a  common  subjective  standard,  — 
utility.  The  desirability  of  the  fish  and  the  labor-cost  of 
obtaining  them  are  comparable  magnitudes,  the  one  being 
utility  (or  desirability)  and  the  other  disutility  (or  un- 
desirability). 

To  change  our  illustration,  let  Robinson  Crusoe  be 
suddenly  placed  on  a  fertile  island  suitable  for  banana 
growing.  He  will  be  able  at  first,  owing  to  the  great  fer- 
tility, to  get  a  high  degree  of  satisfaction  in  consuming 
bananas  by  the  expenditure  of  a  low  degree  of  labor  in 
planting  and  cultivating  the  trees.  But  the  same  objec- 
tions apply  as  before ;  for  the  excess  of  subjective  satisfac- 
tion over  subjective  effort  is  no  more  fixed  than  any  other 
excess  of  return  over  cost,  and  Crusoe  may,  if  inclined,  be 
so  industrious  in  his  raising  of  bananas  as  to  vastly  increase 
the  labor  of  raising  them,  or,  by  satiating  himself  with  them, 
decrease  the  satisfaction  which  they  yield,  or  both.  This 
process  will  proceed  far  enough  to  reduce  the  excess  of  satis- 
faction over  effort  to  such  dimensions  as  Crusoe's  relative 
valuation  of  present  effort  and  future  satisfaction  will 
allow.  The  stopping  point  is  determined  by  him,  not  by 
any  natural  yield  of  the  soil.  The  mere  fact  that  the 
island  is  naturally  fertile,  so  that  labor  is  especially  pro- 
ductive, cannot  determine  the  degree  of  intensive  culture 
which  Crusoe  may  apply  to  it. 

The  same  principles  apply  to  every  unusually  lucrative 
employment.  Man  is  continually  hunting,  as  it  were,  for 
bargains  with  Nature;  but  he  deals  at  Nature's  bargain 
counter  only  up  to  a  definite  point,  —  a  point  decided  upon 
by  him  and  not  by  Nature.  We  cannot  obtain  a  true  and 
complete  explanation  of  interest  without  recourse  to  the 
psychological  element  of  human  choice. 

Those  who  have  made  the  most  successful  use  of  the  cost 
theory  of  interest  are  John  Rae  *  and  Adolphe  Landry,^ 

*  The  Sociological  Theory  of  Capital,  edited  by  Professor  C.  W.  Mix- 
ter,  (Macmillan)  190.5. 

2  L'InUret  du  Capital,  Paris  (Giard  &  Bri^re),  1904. 


38  THE  RATE  OF  INTEREST  [Chap.  Ill 

and  both  of  these  expressly  admit  that  the  ratio  of  return 
to  cost  can  influence  the  rate  of  interest  only  as  the  mar- 
ginal excess  of  return  over  cost  harmonizes  with  the  degree 
of  preference  for  present  over  future  goods.  No  objection 
is  here  offered  to  the  general  reasoning  of  Rae  and  Landry, 
Their  results  and  those  shown  in  the  present  book  are  for 
the  most  part  in  agreement.  The  chief  difference,  in  so 
far  as  the  present  topic  is  concerned,  grows  out  of  the  fact 
that  neither  Rae  nor  Landry  made  use  of  any  definite  theory 
of  income,  the  relation  of  cost  to  income,  and  the  distinc- 
tion between  labor-costs  and  "interactions." 

§6 

Some  economists,  whom  Professor  Bohm-Bawerk  clas- 
sifies as  the  "labor  theorists  of  the  English  school,"  have 
attempted  to  explain  the  rate  of  interest  as  a  sort  of  wage 
for  the  labor  of  producing  capital.  This  theory  is  very 
crude  and  does  not  need  extended  discussion ;  for  it  is  evi- 
dent that  the  labor  which  produces  the  capital  very  seldom 
receives  the  interest.  Suppose  that  a  tree  twenty-five 
years  old  is  worth  $3,  and  was  planted  at  a  cost  of  $1 
worth  of  labor.  The  laborer  was  paid  $1  when  the  tree 
was  planted ;  evidently  not  he,  but  the  capitalist  who  pays 
him,  receives  the  $3  twenty-five  years  later  and  thereby  en- 
joys an  increase  of  value  of  $2.  If  this  $2,  which  is  inter- 
est, is  produced  by  the  laborer  who  planted  the  tree,  why 
does  he  not  get  it  ?  It  is  quite  true  that  the  laborer  pro- 
duces this  "surplus  value,"  and  yet  he  is  forced  to  let 
another  receive  it. 

This  paradox  has  been  made  use  of  by  the  socialists, 
who  maintain  that  interest  ought  to  go  to  the  laborers 
who  produce  the  capital,  but  that  they  are  robbed  of  it  by 
the  capitalist.  This  "exploitation  theory  of  interest"  con- 
sists virtually  of  two  propositions:  first,  that  the  value 
of  any  product  usually  exceeds  its  cost  of  production ;  and, 
secondly,  that  the  value  of  any  product  ought  to  be  exactly 


Sec.  6]  COST  THEORIES  39 

equal  to  its  cost  of  production.  The  first  of  these  proposi- 
tions is  true,  but  the  second  is  false.  Economists  have 
usually  pursued  a  wrong  method  in  answering  the  social- 
ists, for  they  have  attacked  the  first  proposition  instead  of 
the  second.  The  socialist  is  quite  right  in  his  contention 
that  the  value  of  the  product  exceeds  the  cost.  In  fact, 
this  proposition  is  fimdamental  in  the  whole  theory  of  cap- 
ital and  interest.  Ricardo  here,  as  in  many  other  places 
in  economics,  has  been  partly  right  and  partly  wrong.  He 
was  one  of  the  first  to  fall  into  the  fallacy  that  the  value 
of  the  product  was  normally  equal  to  its  cost,  but  he  also 
noted  certain  apparent  "exceptions,"  as  for  instance,  that 
wine  increased  in  value  with  years.  As  a  matter  of  fact, 
as  Bohm-Bawerk  has  fully  shown,  this  increase  of  value, 
instead  of  being  exceptional,  is  universal  in  the  whole 
realm  of  production.  It  is  just  because  the  value  of  a 
product  does  exceed  its  cost  that  there  exists  the  possi- 
bility of  any  perpetual  net  income.^  Not  only,  therefore, 
is  there  no  necessity  that  cost  should  equal  retm'n,  but 
on  the  contrary,  it  never  can  normally  do  so.  By  making 
cost  of  production  a  corner-stone  of  the  theory  of  value, 
the  classical  economists  weakened  their  system  greatly.^ 

In  attempting  to  prove  that  the  laborer  should  receive  the 
whole  product,  the  socialist  thus  stands  on  stronger  ground 
than  has  sometimes  been  admitted.     He  cannot  be  an- 

*  See  Chap.  II  and  its  Appendix,  where  it  is  shown  that  if  each  ma- 
chine costs  exactly  what  it  returns,  and  if  the  up-keep  of  a  group  of 
machines  is  maintained,  the  net  annual  income  from  the  group  is  zero. 

'  Besides  the  error  that  the  cost  of  production  theory  omits  the 
interest  element,  there  was  the  error  that  most  costs  of  production  — 
all  "interactions,"  in  fact  —  are  themselves  not  the  cause  but  the 
result  of  value,  being  future  values  discounted.  See  The  Nature  of  Capi- 
tal and  Income,  Chaps.  X,  XIV,  XVII.  This  objection  to  the  cost 
theory  of  value  does  not  apply  to  labor-cost;  but  even  labor-cost  is 
not  a  necessary  or  universal  accompaniment  of  value.  A  mineral 
spring  may  produce  a  valuable  water  without  labor-cost.  Land 
also  is  largely  costless  except  for  the  cost  of  transferring  it,  which  is 
an  "interaction."  Other  classical  examples  of  articles  which  have 
no  cost  of  production  are  autographs  of  Milton  and  similar  memora- 
bilia. 


40  THE  RATE  OF  INTEREST  [Chap.  Ill 

swerecl  offhand  by  saying  that  capital  aids  labor,  and  that 
the  owner  of  a  plow  deserves  an  interest  payment  for  its 
use  quite  as  truly  as  the  laborer  who  operates  the  plow 
deserves  wages  for  his  labor.  Tlie  socialist  contends  that 
the  payment  for  the  use  of  the  plow  should  belong,  not  to 
the  man  who  holds  it,  but  to  the  man  who  made  it.  He  is 
quite  correct  in  believing  that  the  value  of  the  uses  of  the 
plow  is  entirely  due  to  the  laborers  who  made  it,  but 
that,  nevertheless,  the  capitalist,  not  the  laborer,  enjoys  the 
value  of  these  uses.  The  capitalist  is,  as  a  matter  of  fact, 
always  living  on  the  product  of  past  labor.  A  millionaire 
who  gets  his  income  from  railroads,  ships,  and  houses,  all 
products  of  labor,  is  reaping  what  labor  sowed.  Tlie  capi- 
talists of  to-day  are  receiving  compound  interest  on  the 
labor  of  yesterday. 

§  7 

But  it  does  not  follow  that  in  this  any  injustice  has  been 
done  to  the  laborer.  Let  us  revert  to  the  case  of  the  tree 
which  was  planted  with  $1  worth  of  labor,  and  25  years 
later  was  worth  $3.  The  socialist  virtually  asks,  Vvliy 
should  not  the  laborer  receive  $3  instead  of  $1  for  his  work  ? 
The  answer  is  that  he  may  receive  it,  provided  he  will  wait 
25  years  for  the  $3  !    As  Bohm-Bawerk  says :  ^  — 

"The  perfectly  just  proposition  that  the  laborer  should  receive 
the  entire  value  of  his  product  may  be  understood  to  mean  either 
that  the  laborer  should  7iow  receive  the  entire  present  value  of  his 
product,  or  should  receive  the  entire  future  value  of  his  product 
in  the  future.  But  Rodbertus  and  the  socialists  expound  it  as  if 
it  meant  that  the  laborer  should  now  receive  the  entire  future 
value  of  his  product." 

To  take  another  example :  if  a  number  of  laborers  work 
upon  a  railroad  which  requires  5  years  before  it  can  be 
completed,  and  which,  when  completed,  is  worth  $7,000,000, 
there  is  no  reason,  if  the  laborers  are  willing  to  wait  until 
the  road  is  completed,  that  they   should   not   own   and 

*  Capital  and  Interest,  p.  342. 


Sec.  7]  COST  THEORIES  41 

operate  it.  They  would  then  be  receiving,  in  the  future, 
the  future  value  of  their  product.  If,  however,  they  are 
paid  at  the  time  their  work  is  being  done,  they  may  be 
paid  in  one  of  two  ways.  One  is  by  having  assigned  to  them 
such  parts  of  the  road  as  they  have  created  so  that  they  may 
retain  the  same  until  it  is  a  finished  product  to  return 
income  to  them  in  future  years.  The  other  method,  and 
the  one  which  they  much  prefer,  is  to  be  paid  in  cash, 
convertible  immediately  into  food,  clothes,  and  other  en- 
joyable income.  Under  these  circumstances  the  road, 
which  is  to  be  worth  $7,000,000,  will  be  paid  for  in  wages, 
not  by  $7,000,000,  but  by,  say,  $5,000,000,  distributed  at 
the  rate  of  $1,000,000  a  year  for  the  5  years  required  to 
build  the  road. 

Socialists  would  cease  to  think  that  this  is  extortion 
if  they  would  try  the  experiment  of  sending  a  colony  of 
laborers  into  the  unreclaimed  lands  of  the  West,  letting 
them  develop  and  irrigate  those  lands  and  build  railways 
on  them,  unaided  by  borrowed  capital.  The  colonists 
would  find  that  interest  had  not  disappeared  by  any  means, 
but  that  by  waiting  they  had  themselves  reaped  the  benefit 
of  it.  Tliey  would  need  to  wait,  let  us  say,  5  years  before 
their  railway  was  completed.  At  the  end  of  that  time 
they  would  own  every  cent  of  its  earnings,  and  no  ''capi- 
tahst"  could  be  accused  of  robbing  them  of  it.  But  they 
would  find  that,  in  spite  of  themselves,  they  had  now 
become  capitalists,  and  they  had  become  so  by  stinting  for 
those  5  years,  instead  of  receiving  in  advance,  in  the  shape 
of  food,  clothing,  and  other  real  income,  the  discounted 
value  of  the  raih'oad.  This  example  was  almost  literally 
realized  in  the  case  of  the  Mormon  settlement  in  Utah. 
Those  who  went  there  originally  possessed  little  capital, 
and  did  not  pay  interest  for  the  use  of  other  persons'  cap- 
ital. They  created  their  capital,  and  passed  from  the 
category  of  ''laborers"  to  that  of  ''capitalists."  It  will  be 
seen  that  capitalists  are  not  robbers  of  labor,  but  labor- 
brokers  who  buy  work  at  one  time  and  sell  its  products  at 


42  THE  RATE  OF  INTEREST  [Chap.  Ill 

another.  Their  profit  on  the  transaction  (or  rather,  that 
part  of  it  which  is  interest)  is  due  to  the  time  elapsing 
between  the  labor  and  its  return  to  the  capitalist. 


§8 

Among  those  who  have  attempted  to  justify  interest- 
taking  on  a  labor  basis  is  a  peculiar  group  of  theorists  who 
maintain  that  interest  does  actually  go  to  the  laborer  —  not 
the  laborer  who  produces  the  capital,  but  the  laborer  who 
manages  it.  In  other  words,  the  "entrepreneur,"  "imder- 
taker,"  or  "enterpriser"  is  the  one  who  creates  interest 
and  therefore  deserves  it.  This  is  another  of  the  many  at- 
tempts to  maintain  that  every  economic  product  must  be 
a  mere  equivalent  for  some  corresponding  labor-outgo. 
The  only  evidence  the  adherents  of  this  school  can  offer 
for  the  truth  of  their  theory  is,  however,  that  capital  can 
produce  nothing  without  proper  management.  If,  they 
say,  no  one  lifts  a  finger  to  make  capital  productive,  it  will 
not  be  productive,  and  the  man  who  plans,  organizes,  and 
controls  the  use  of  capital  is  the  one  who  creates  interest 
and  ought  to  receive  it.  This  theory,  however,  is  evidently 
fallacious,  if  not  self-destructive.  For  the  person  who 
receives  interest,  par  excellence,  is  not  the  active  "  entrepre- 
neiu-,"  but  his  "sleeping  partner."  If  the  active  capitalist 
produces  the  interest  on  the  capital  he  borrows  from  his 
sleeping  partner,  who  "does  not  lift  a  finger,"  why  does  he 
surrender  any  of  it  to  that  partner  ?  Is  the  sleeping  part- 
ner "exploiting"  his  active  associate?  Of  course  it  is 
true  that  the  mere  investor  could  get  no  interest  were  it 
not  for  some  intelligent,  active  management  of  capital. 
But  this  management  is  paid  for  in  the  shape  of  entre- 
preneur's profits.  The  mere  fact  that  the  entrepreneur's 
work  is  usually  indispensable  to  the  production  of  income 
would  not  justify  his  receiving  all  of  that  income.  In  fact, 
we  may  conversely  state  that  the  capital  intrusted  to  the 


Sec.  9]  COST  THEORIES  43 

entrepreneur  is  quite  as  indispensable  to  him  as  is  his  work 
to  the  inactive  capitalist. 

§  9 

So  determined  have  been  the  attempts  to  justify  interest 
on  the  ground  of  some  cost  of  production  that,  in  the  ab- 
sence of  any  other  item  which  can  be  called  cost,  a  special 
constructive  cost  called  "abstinence"  or  "waiting"  has 
been  invoked  to  meet  the  emergency.  Certain  French 
economists  have  even  gone  so  far  as  to  call  this  the  "labor 
of  saving,"  Tlie  abstinence  theory  in  its  various  forms 
holds  that  the  capitalist,  by  abstaining  from  the  consump- 
tion of  his  capital,  obtains  a  reward  in  the  shape  of  interest. 

The  abstinence  theory  bears  a  close  resemblance  to  the 
"agio"  theory  of  interest,  which  is  believed  by  the  writer 
to  be  essentially  correct.  In  fact,  it  has  been  claimed  by 
some  writers  that  the  abstinence  theory  differs  from  the 
agio  theory  merely  in  words.  This  claim  is  perhaps  true 
of  certain  versions  of  the  theory,  and  against  these  no  criti- 
cism need  here  be  offered,  unless  it  be  a  verbal  one.  If  by 
saymg  that  interest  is  the  reward  of  waiting  or  abstinence 
it  is  only  meant  that  men  prefer  not  to  wait  for  the  future, 
but  to  enjoy  the  present,  the  only  objection  which  need  be 
offered  is  that  the  mode  of  statement  is  somewhat  unhappy ; 
it  implies,  apparently,  that  futm'e  rewards  are  caused  by 
making  present  sacrifices,  rather  than  that  present  sacri- 
fices are  caused  by  the  prospect  of  future  rewards. 

But  in  the  sense  in  which  the  abstinence  theory  is  usually 
held,  it  differs  from  the  agio  theory  not  only  in  words  but 
in  essence.  As  Bohm-Bawerk  has  shown,  it  assumes  that 
"abstinence"  is  an  independent  item  in  cost  of  production, 
to  be  added  to  the  other  costs  and  to  be  treated  in  all  ways 
like  them.  With  this  proposition  issue  is  here  joined.  If 
"abstinence"  or  "waiting"  or  "labor  of  saving"  is  in  any 
sense  a  cost,  it  is  certainly  a  cost  in  a  very  different  sense 
from  all  other  items  which  have  previously  been  con- 


44  THE  RATE  OF  INTEREST  [Chap.  Ill 

sidered  as  costs.  An  illustration  will  make  clear  the  dif- 
ference between  true  costs  and  the  purely  constructive 
cost  of  waiting.  According  to  the  theory  that  waiting  is 
a  cost,  if  planting  a  sapling  costs  $1  worth  of  labor,  and  in 
25  years,  without  further  expenditure  of  labor,  this  sapling 
becomes  worth  $3,  this  $3  is  a  mere  equivalent  for  the  entire 
cost  of  producing  the  tree.  The  items  in  this  cost  are,  it 
is  claimed,  $1  worth  of  labor  and  $2  worth  of  "waiting." 

According  to  the  theory  of  the  present  book,  however,  the 
cost  of  producing  the  tree  is  the  $1  worth  of  labor,  and 
nothing  more.  The  value  of  the  tree,  $3,  exceeds  that 
cost  by  a  surplus  of  $2,  the  existence  of  which  as  interest 
it  is  our  business  to  explain.  At  first  it  would  seem  a  mere 
matter  of  words  whether  we  call  the  $2  a  surplus  above  cost, 
or  an  item  constituting  another  cost,  known  as  "waiting." 
But  examination  will  show  that  the  two  so-called  "costs" 
are  radically  different. 

If  waiting  is  a  cost  like  other  costs,  it  should  be  subject 
to  the  law  of  discount,  according  to  which  the  capital- 
value  of  any  article  of  wealth  is  equal  to  the  discounted 
value  of  its  expected  income  less  the  discoimted  value  of  its 
expected  outgo.  The  value  of  the  tree  which  has  just  been 
mentioned,  taken,  say,  at  the  end  of  14  years,  will  actually 
be  about  $2,  and  this  is  the  discounted  value  of  the  $3  of 
income  which  the  tree  will  yield  at  the  end  of  eleven  more 
years.  According  to  our  own  theory,  this  $3  is  the  only 
future  item  of  income  or  outgo.  But  according  to  the 
theory  here  criticised,  besides  this  positive  item  of  income, 
$3  due  in  eleven  years,  we  have  to  deal  with  a  series  of 
eleven  negative  items  called  "waiting,"  distributed  through 
these  eleven  years,  and  amounting  to  the  interest, — 
about  10  cents  for  the  fii'st  year  and  gradually  increasing  to  15 
cents  for  the  last  year.  Now  if  these  costs  really  exist, 
they  ought  to  be  discounted  and  their  discounted  value 
deducted  from  the  discounted  value  of  the  S3  of  expected 
income.  But  we  should  then  have  to  assign  a  value  to  the 
tree  not  of  $2,  as  it  actually  is,  but  of  about  $1,  which  is 


Sec.  10]  COST  THEORIES  45 

erroneous.     If  the  waiting-items  were  bona  fide  annual  costs, 

—  like,  for  instance,  actual  labor-costs  of  pruning  the  trees, 

—  the  process  of  discount  would  properly  be  applied  to 
them.  The  fact  that  it  cannot  be  applied  to  the  so-called 
"cost  of  waiting"  without  leading  to  an  erroneous  result  is 
a  proof  that  the  "cost  of  waiting"  differs  radically  from 
true  costs. 

Thus,  the  theory  that  waiting  is  a  cost  or  outgo  is  a  fal- 
lacy exactly  the  inverse  of  the  fallacy  that  saving  is  income 
explained  in  The  Nature  of  Capital  and  Income.^  Both 
have  to  deal  with  the  increase  of  capital- value ;  the  one 
theory  regards  this  increase  as  income,  the  other  as  outgo. 
As  a  matter  of  fact,  it  is  neither  income  nor  outgo,  but 
increase  of  capital  only. 


§  10 

As  an  answer  to  the  objection  just  urged  against  treating 
waiting  as  a  cost,  namely,  that  it  cannot  be  discounted,  it 
might  be  pointed  out  by  the  abstinence  theorists  that  while 
waiting-cost  is  certainly  not  a  discountable  cost,  its  inclu- 
sion in  the  list  of  costs  obviates  the  necessity  of  discounting 
the  other  items  of  cost  or  of  income.  If  all  income  and  all 
cost  items,  including  waiting,  are  counted  at  full  value, 
capital  may  be  valued  simply  by  taking  their  net  sum, 
without  subjecting  any  item  to  the  discounting  process. 
To  count  "waiting"  as  a  cost,  then,  appears  as  an  alterna- 
tive method  of  keeping  accounts.  Accepting  this  answer 
for  the  sake  of  argument,  we  observe  that  while  it  obviates 
the  objection  to  the  abstinence  theory  of  cost  so  far  as  its 
application  to  capital  value  is  concerned,  it  leaves  objec- 
tions equally  great  to  its  application  to  income.  If  wait- 
ing is  a  cost  like  other  items,  it  must  be  included  on  the 
outgo  side  of   the  income  account.     To  show  how   this 

*  Chap.  XIV.  Cf.  as  to  the  fallacy  here  considered,  Bohm-Bawerk, 
Recent  Literature  on  Interest  (Macmillan) ,  1903,  p.  35  n. 


46 


THE  RATE  OF  INTEREST 


[Chap.  Ill 


would  apply  to  the  cost  of  the  tree,  the  following  table  is 
presented :  — 


Income 


1st  year  

2d  year    

3d  year    

14th  year      .... 

»JC  7^  0ji  7j^  ?|s  ?J5  ?JC 

25th  year,  from  sale 
of  tree      .... 

Total     .... 


00.00 

00.00 

00.00 

*  * 

00.00 

*  * 

3.00 


3.00 


Outgo 

Net 
Income 

Labor 
"Waiting" 
"Waiting" 
"Waiting" 

7fi                    1*                     'IS                    'I* 

1.00 

.05 

.05 

.05 
* 

"Waiting" 
*    *    *    * 

.10 
* 

"Waiting" 

.15 

3.00 

00.00 

Capital 

Value  at 

End  of 

Year 


1.05 
1.10 

1.15 

*  * 

2.00 

*  * 

3.00 


According  to  this  method  of  accounting,  we  see  that 
during  the  year  in  which  the  sapling  is  planted  its  cost  con- 
sists of  labor  to  the  extent  of  $1,  expended,  let  us  say,  at 
the  beginning  of  the  year,  and  5  cents'  worth  of  waiting 
suffered  during  the  course  of  the  year.  During  the  second 
year  a  waiting  cost  of  about  the  same  amount  is  incurred, 
and  so  on  for  each  succeeding  year,  the  cost  of  waiting 
gradually  increasing  as  the  tables  of  compound  interest 
would  indicate,  until  in  the  fourteenth  year  it  amounts  to 
10  cents,  and  in  the  twenty-fifth  year  to  15  cents.  The 
total  cost  for  the  25  years  will  then  be  $3,  and  the 
return  to  the  planter  at  the  end,  from  the  sale  of  the  tree, 
will  also  be  $3.  Consequently,  if  we  take  the  whole 
period  from  the  first  application  of  labor  to  the  final  sale  of 
the  tree,  the  net  income  will  be  zero.  This  result  is,  to 
say  the  least,  somewhat  surprising,  but  not  so  much  so  as 
some  other  results  of  the  same  bookkeeping,  as  the  fol- 
lowing additional  examples  will  show. 

Suppose  a  person  owns  an  annuity  amounting  to  $100  a 
year  for  10  years.      According  to  any  ordinary  method 


Sec.  10] 


COST  THEORIES 


47 


of  keeping  accounts,  his  income  consists  of  this  SlOO  a  year 
each  year.  But  if  we  count  the  waiting  as  a  cost,  we  shall 
find  that  the  income  for  each  year  is  less  than  $100.  The 
owner  of  such  an  annuity  will,  during  the  first  year,  have 
to  suffer  "waiting"  to  the  extent  of  $39,  supposing  interest 
is  at  5  per  cent. ;  for  this  is  the  increase  in  value  of  his  an- 
nuity during  that  year,  due  to  his  waiting  for  the  future 
instalments  of  income  of  which  his  annuity  consists.^  His 
net  income  during  that  year,  therefore,  according  to  such 
accounting,  is  not  $100,  but  $100 -$39,  or  $61.  During 
the  second  year  his  income  is  somewhat  greater,  for  the 
cost  of  "waiting"  is  only  $35.  His  net  income  is,  therefore, 
$100  — $35,  or  $65.  Similar  computations  carried  out  for 
succeeding  years  result  in  the  following  table :  — 


Capital 

Net 

Value  at 

Income 

Outgo 

Income 

Beginning 

OF  Year 

1st  year 

money, 

$100 

"Waiting" 

1  39 

$  61 

$772 

2d  year 

money, 

100 

"Waiting" 

35 

65 

711 

3d  year 

money, 

100 

"Waiting" 

32 

68 

646 

4th  year 

money, 

100 

"Waiting" 

29 

71 

578 

5th  year 

money, 

100 

"Waiting" 

25 

75 

507 

6th  year 

money, 

100 

"Waiting" 

22 

78 

432 

7th  year 

money, 

100 

"Waiting" 

18 

82 

354 

8th  year 

money, 

100 

"Waiting" 

14 

86 

272 

9th  year 

money 

100 

"Waiting" 

9 

91 

186 

10th  year 

money, 

100 

"Waiting" 

5 

95 

95 

$1000 

$228 

$772 

Is  it  good  bookkeeping  to  introduce  a  new  and  strange 
element  of  cost  which  results  in  making  the  net  income 
of  the  annuitant  not  the  $100  which  he  actually  receives, 

*  This  is  evident,  since  the  value  of  his  annuity,  capitalized  at  5  per 
cent.,  reckoned  at  the  beginning,  is  $772,  whereas,  reckoned  at  the  end 
of  the  first  year,  before  his  $100  is  paid,  it  is  $811. 


48  THE  RATE  OF  INTEREST  [Chap.  Ill 

but  the  sums  given  in  the  table;  namely,  $61,  $65,  $68, 
and  so  forth  ? 

To  push  this  criticism  to  the  limit,  let  us  finally  consider 
a  perpetual  annuity  of  $100  a  year.  In  this  case  we  shall 
find  that  the  "cost  of  waiting"  each  year  is  $100;  for 
the  value  of  such  an  annuity,  reckoned  at  5  per  cent.,  is 
$2000  reckoned  at  the  beginning  of  each  year,  and  $2100 
reckoned  at  the  end.  If  this  cost  of  waiting  is  to  be  re- 
garded as  a  deduction  from  income,  like  other  costs,  we 
are  forced  to  conclude  that  the  owner  of  such  a  perpetual 
annuity  receives  each  year  no  income  whatever !  For,  if 
we  deduct  from  the  $100  of  money-income  the  $100  of 
waiting,  the  remainder  each  year  is  zero ! 

It  may  be  said  that  we  have  not  always  a  mere  annuity 
to  deal  with  but  a  definite  capital  such  as  a  house  or  a 
factory  which  has  involved  cost  in  its  construction  and 
the  "  sacrifice "  of  waiting  for  an  income,  whereas  the 
capital  might  have  been  consumed  at  once.  In  all  such 
cases,  however,  we  are  dealing  with  the  very  same  prin- 
ciple. The  possession  of  the  house  or  factory,  like  the 
title  to  the  annuity,  is  valuable  only  because  of  the  service 
or  the  income  which  it  is  expected  to  yield.  If  there  is 
for  the  house  or  factory  an  initial  labor-cost  or  expense, 
this  is  also  true  of  the  annuity.  On  the  other  hand,  the 
one  as  well  as  the  other  may  come  by  inheritance  and  so 
involves  no  cost  to  its  owner.  What  it  is  desired  to  em- 
phasize is  that  in  any  case  the  present  value  is  the  dis- 
counted value  of  the  expected  future  services  or  income 
and  that  it  is  not  any  sacrifice  or  cost  of  waiting  which 
produces  this  value  but  that,  on  the  contraiy,  it  is  the 
existence  of  this  future  value  which  prompts  the  waiting. 


§  11 

It  is  obvious  that  the  theory  which  calls  "waiting"  a 
cost  has  worked  out  its  own  absurdity.     The  most  that  can 


Sec.  11]  COST  THEORIES  49 

be  said  in  its  favor  is  that  it  makes  the  capital-value  of 
any  article  equal  to  its  cost  of  production.  The  idea  that 
the  value  of  an  article  should  equal  its  cost  seems  to  pos- 
sess a  certain  fascination  for  many,  if  not  most,  students  of 
economics.  That  it  is  false  has  been  sufficiently  shown 
by  Bohm-Bawerk  through  reasoning  somewhat  similar  to 
the  foregoing.  Tliat  it  is  absurd  when  carried  to  its  logical 
conclusion  is  evident  when  we  consider  what  happens  if  the 
same  method  of  bookkeeping  is  carried  out  with  respect 
to  the  future  as  well  as  the  past.  It  is  a  poor  rule  which 
will  not  work  both  ways.  This  rule,  applied  to  future 
expected  income  and  outgo,  yields  the  strange  result  that 
the  capital  value  of  any  article  is  normally  not  less  than, 
but  equal  to,  the  expected  income.  Thus,  to  revert  to 
the  case  of  the  tree,  let  us  take  its  value  at  the  end  of 
14  years.  It  is  then  worth  $2,  which,  in  the  parlance 
of  the  abstinence  theorists,  is  equal  to  its  previous  cost 
of  production,  consisting  of  $1  worth  of  labor  plus  $1 
worth  of  waiting  during  the  14  years.  It  is  also,  in 
like  manner,  equal  to  the  future  income  to  be  derived 
from  it,  which  consists  of  $3  worth  of  actual  receipts 
from  the  sale  of  the  tree,  due  at  the  end  of  eleven 
more  years,  less  the  cost  of  waiting  for  those  $3,  which 
amounts  to  $1. 

In  the  same  way,  the  ten-year  annuitant  just  consid- 
ered has,  at  the  beginning,  property  worth  $772.  This, 
according  to  any  proper  bookkeeping,  is  the  discounted 
value  of  the  future  income  of  $100  a  year  for  10  years,  the 
total  amount  of  which  is  $1000.  But,  according  to  the 
abstinence  theorists,  the  income  which  he  receives  for  the 
whole  period  is,  as  has  been  shown,  not  this  $1000,  but 
$772,  which  is  just  equal  to  the  value  of  the  property. 
Pursuing  the  method  of  limits,  we  find  that  for  the  owner 
of  a  perpetual  annuity  the  same  proposition  would  hold 
good.  According  to  the  true  and  ordinary  method  of  reck- 
oning, the  total  income  from  such  an  annuity  is  infinity, 
although  its   present   capital   value   is   only  $2000.     But 


50  THE  RATE  OF  INTEREST  [Chap.  Ill 

according  to  the  abstinence  theorists  the  income  itself  is 
not  infinite,  but  only  $2000.' 

Those  who  are  enamored  of  the  simplicity  and  neatness 
of  the  formula  of  the  abstinence  theorists,  by  which  the 
capital  value  is  not  greater  than  past  cost  of  production, 
but  exactly  equal  to  it,  can  scarcely  be  attracted  by  the 
exaggerated  simplicity  of  the  inverse  theorem  which  is 
also  involved ;  namely,  that  the  capital  value  of  any  future 
expected  income  is  not  less  than  that  income,  but  exactly 
equal  to  it  also. 

§  12 

The  fallacy  of  the  abstinence  theorists  lies  in  the  simple 
fact  that  waiting  has  no  independent  existence  as  a  "cost." 
We  can  never  locate  it  in  time,  nor  estimate  its  amount, 
without  first  knowing  some  other  more  tangible  costs. 
Waiting  means  nothing  unless  there  is  something  waited 
for,  and  the  cost  of  waiting  can  only  be  estimated  in  pro- 
portion to  the  magnitude  of  what  is  waited  for. 

It  will  doubtless  take  a  long  time  for  many  to  accept  the 
doctrine  that  the  value  of  capital  is  not  only  less  than  its 
future  expected  income,  but  normally  greater  than  its  past 
cost.  Even  to  those  who  do  not  formally  accept  any  cost 
theory  of  interest,  the  interest  itself  will  seem  in  some 
sense  to  be  a  cost;  and  in  most  books  on  economics,  in- 
terest, however  explained,  is  regarded  as  one  of  the  costs 
of  production.  It  is  true  that  for  a  debtor  who  pays  in- 
terest, the  interest  is,  to  him,  a  real  cost,  and  is  debited  on 

•  Lest  the  non-mathematical  reader  should  be  puzzled  by  this 
result,  which  seems  to  contradict  the  fact  already  brought  out,  that 
under  the  pseudo-reckoning  of  the  abstinence  theorists  the  net  in- 
come is  zero  every  year,  it  must  be  remembered  that  this  zero  income 
is  repeated  an  infinite  number  of  times,  and  that  when  we  deal  with 
infinity  we  can  get  reliable  results  only  by  the  method  of  limits. 
The  mathematical  reader  will  find  no  difficulty  in  showing,  by  the 
method  of  limits,  that  there  is  a  "remainder  term"  which  will,  in 
the  supposed  accounting,  make  the  total  income  distributed  through 
all  eternity  simply  equal  to  the  capital  value,  $2000. 


Sec.  13]  COST  THEORIES  51 

his  books.  But  we  need  only  to  be  reminded  of  the  debit 
and  credit  bookkeeping  which  was  considered  at  length  in 
The  Nature  of  Capital  and  Income  to  see  that  this  item  is 
counterbalanced  on  the  books  of  the  creditor,  to  whom  this 
interest  is  by  no  means  a  cost,  but  an  item  of  income.  For 
society  as  a  whole,  therefore,  even  in  the  case  of  interest 
which  is  explicitly  paid,  it  cannot  be  said  that  it  consti- 
tutes a  cost  of  production.  In  the  case  of  a  person  who 
works  with  his  own  capital,  the  truth  of  this  statement  is 
even  more  evident.  Economists  who  state  that  the  inde- 
pendent capitalist  must  charge  off  interest  as  one  of  his 
costs  of  production  seem  to  forget  that  such  self-paid 
interest  must  be  charged  back  again  as  income  also.  The 
fallacy  of  assuming  that  interest  is  a  cost  is  doubtless  due 
to  the  habit  of  regarding  production  from  the  point  of 
view  of  the  "  enterpriser."  Since  he  usually  pays  interest, 
he  comes  to  think  of  it  purely  as  a  cost. 

We  have  devoted  considerable  space  to  the  refutation  of 
the  abstinence  theory,  because  its  errors  are  so  subtle  and 
insidious  as  to  beguile  many  of  the  best  and  most  wary 
of  economists. 


§  13 


The  results  of  the  present  chapter  may  be  summed  up 
by  grouping  the  cost  theories  under  two  heads :  those 
which  regard  interest  as  in  some  sense  a  cost;  and  those 
which  regard  interest  as  a  surplus  above  cost.  As  we  have 
seen,  the  contention  of  the  first  group  is  erroneous,  whether 
the  concept  of  cost  employed  is  the  "cost  of  producing  capi- 
tal," the  "cost  of  managing,"  organizing,  or  investing  it, 
or  the  purely  constructive  cost  of  "waiting,"  "abstinence," 
or  "labor  of  saving."  The  contention  of  the  second  group, 
which  considers  interest  as  a  surplus  above  cost,  is  correct; 
but  the  explanations  which  are  given  of  this  surplus  are  in- 
correct, or  at  any  rate,  incomplete,  whether  those  explana- 


52  THE  RATE  OF  INTEREST  [Chap.  Ill 

tions  take  the  fanciful  form  of  the  socialists  that  interest  is 
extortion,  or  the  mere  statement  of  fact  of  the  cost  produc- 
tivity theories,  that  nature  yields  a  surplus  above  cost.  In 
this  last  statement,  however,  lies  the  only  grain  of  truth 
which  can  be  ascribed  to  the  cost  theories.  Although 
nature  does  not  of  herself  yield  a  fixed  surplus  above  cost, 
which  may  be  called  interest,  she  offers  a  series  of  such 
opportunities  of  getting  a  surplus,  of  which  opportunities 
man  takes  advantage,  and  with  respect  to  which  he  adjusts 
his  efforts  to  his  returns  until  the  surplus  yielded  corre- 
sponds to  his  subjective  preference  for  present  over  future 
goods.  In  other  words,  just  as  in  the  case  of  the  theories 
based  on  productivity,  we  find  that  the  theories  based  on 
cost  have  an  element  of  truth  only  as  far  as  the  oppor- 
tunities presented  by  nature  are  reviewed  in  the  mind  of 
man  and  decided  upon  according  to  his  time  preference. 


CHAPTER   IV 


bohm-bawerk's  theory 


§  1 

In  the  preceding  three  chapters  the  most  common  of 
the  existing  theories  of  interest  have  been  stated  and  criti- 
cised. There  remains  one,  however,  which  has  received 
a  large  degree  of  cmrency  among  economists.  Hitherto, 
in  order  to  condense  our  review,  we  have  employed  the 
impersonal  method  and  have  rarely  discussed  the  special 
interpretations  which  individual  writers  have  made  of 
the  several  theories.  In  the  present  chapter,  however,  we 
shall  depart  from  this  practice.  The  reason  for  criti- 
cising Bohm-Bawerk's  specific  theory  is  that,  unlike  the 
theory  of  any  other  individual  writer,  it  has  become  widely 
accepted.  Capital  and  Interest  and  The  Positive  Theory 
of  Capital  have  become  economic  classics.  There  can  be 
no  question  that  they  deserve  the  high  esteem  in  which 
they  are  held,  for  they  contain  the  material,  both  in  their 
destructive  criticism  and  in  their  constructive  argument,  for 
a  correct  theory  of  interest.  For  the  most  part,  Bohm- 
Bawerk's  work  will  doubtless  always  stand.  At  only  one 
vital  point  do  we  regard  it  as  defective. 

Bohm-Bawerk's  theory  is  called  by  him  the  "  agio  theory" 
of  interest,  since  it  finds  the  essence  of  the  rate  of  interest 
in  the  agio  or  premium  on  present  goods  when  exchanged 
for  future  goods.  This  theory  is  in  the  main  accepted  by 
the  present  writer  as  the  natural  and  proper  starting- 
point  for  any  rational  discussion  of  the  subject.  Bohm- 
Bawerk  has  presented  the  agio  theory  clearly  and  forcibly, 
and   has   disentangled   it   from   the   crude   and  incorrect 

53 


54  THE  RATE  OF  INTEREST  [Chap.  IV 

notions  with  which  it  had  previously  been  associated.  It 
is  only  when  he  attempts  to  add  to  it  his  special  feature 
of  a  "technical  superiority  of  present  over  future  goods" 
that  he  has  impaired  rather  than  improved  it. 

The  agio  theory  may  be  said  to  have  been  foreshadowed 
by  mediaeval  writers,  some  of  whom  stated  that  interest 
could  be  justified  by  mora  or  "delay";  and  the  theory 
appears  in  a  crude  form  in  the  abstinence  theories  of  Senior 
and  others,  which  were  discussed  in  the  preceding  chapter. 
In  a  more  definite  form  it  was  advanced  by  John  Rae  in 
1834,  in  a  work  which  has  hitherto  received  far  less  atten- 
tion than  it  deserved ;  ^  and  in  a  less  complete  form,  and 
quite  independently  of  Rae,  by  Jevons,^  Sax,^  and  Laun- 
hardt.^  But  excepting  Rae,  none  of  these  writers  can 
compare  with  Bohm-Bawerk  for  the  thoroughness  with 
which  the  theory  is  worked  out. 

Bohm-Bawerk  distinguishes  two  problems:  (1)  Why 
does  interest  exist?  and  (2)  What  determines  any  par- 
ticular rate  of  interest?  In  answer  to  the  first  problem, 
he  states  virtually  that  this  world  is  so  constituted  that 
most  of  us  prefer  present  goods  to  future  goods  of  like  kind 
and  number.  This  preference  is  due,  according  to  Bohm- 
Bawerk,    to   three   circumstances:     (1)    the   "perspective 

*  Bohm-Bawerk  reintroduced  independently  the  main  argument 
of  Rae.  Several  years  later  Rae's  book  was  unearthed  and  brought 
into  prominence  by  Professor  C.  W.  Mixter.  The  original  being  out 
of  print,  Professor  Mixter  has  edited  a  reprint,  rearranged  for  modern 
readers,  under  the  new  title,  The  Sociological  Theory  of  Capital  (Mac- 
millan),  1905.  Rae's  work  labored  under  the  disadvantage,  compared 
with  Bohm-Bawerk's,  of  being  written  before  the  modern  theory  of 
value  had  been  expounded.  Its  shortcomings  are  chiefly  due  to  this 
fact.  On  the  other  hand,  it  surpasses  Bohm-Bawerk's  treatise  in  some 
respects,  notably  in  its  treatment  of  invention.  See  Bohm-Bawerk's 
comments  on  Rae  in  Recent  Literature  on  Interest  (Macmillan),  1903, 
and  the  reply  by  Mixter,  "Bohm-Bawerk  on  Rae,"  Quarterly  Journal 
of  Economics,  May,  1902,  pp.  385-412. 

*  Theory  of  Political  Economy,  London,  3'*  ed.  (Macmillan),  1888. 
'  Grundlegung  der  theoretischen  Staatswirthschaft,  Vienna,  1887. 

*  Mathematische  Begriindung  der  Volkswirtschaftslehre,  Leipsic, 
1885. 


Sec.  2]  BOHM-BAWERK'S  THEORY  55 

underestimate"  of  the  future,  by  which  is  meant  the  fact 
that  future  goods  are  less  clearly  perceived  and  therefore 
less  resolutely  striven  for  than  those  more  immediately 
at  hand;  (2)  the  relative  inadequacy  of  the  "provision" 
for  present  wants  as  compared  with  the  provision  for  future 
wants,  or  in  other  words,  the  relative  scarcity  of  present 
goods  compared  with  future  goods;  (3)  the  "technical 
superiority"  of  present  over  future  goods,  or  the  fact,  as 
Bohm-Bawerk  conceives  it,  that  the  "roundabout"  or 
"capitalistic"  processes  of  production  are  more  remu- 
nerative than  those  which  yield  immediate  retm'ns. 

The  first  two  of  these  three  circumstances  are  undoubtedly 
pertinent,  and  will  be  incorporated,  under  a  somewhat 
different  form,  in  the  theory  of  the  present  book.  It  is 
the  third  circumstance  —  the  so-called  technical  superiority 
of  present  over  future  goods  —  which  we  believe  to  contain 
essential  errors. 

§  2 

According  to  Bohm-Bawerk,  labor  invested  in  long 
processes  of  production  will  yield  larger  retm-ns  than  labor 
invested  in  short  processes,  and  will  therefore  confer  a 
"technical  advantage"  upon  those  who  have  the  command 
of  that  labor.  In  the  reasoning  by  which  Bohm-Bawerk 
attempts  to  prove  this  "technical  superiority,"  there  are 
three  principal  steps.  The  first  consists  of  postulating 
an  "average  production  period"  representing  the  length 
of  the  productive  processes  of  the  community;  the  second 
consists  of  the  proposition  that  the  longer  this  average 
production  period,  the  greater  will  be  the  product;  and 
the  third  consists  in  the  conclusion  that  in  consequence  of 
this  greater  productiveness  of  lengthy  processes,  present 
goods  possess  a  "technical  superiority  "  over  futm^e  goods. 

We  shall  endeavor  to  show  that  the  third  of  these  steps 
contains  a  fatal  error.  The  first  step  also  is  not  wholly 
satisfactory. 


56  THE  RATE  OF  INTEREST  [Chap.  IV 

A  serious  defect  in  Bohm-Bawerk's  concept  of  an  aver- 
age production  period  is  that  it  lacks  sufficient  definiteness 
to  form  a  basis  for  the  reasoning  that  he  attempts  to  base 
upon  it.  He  begins  by  stating  that  every  article  is  the 
result  of  the  cooperation  of  land  and  labor,  and  (abstract- 
ing the  element  of  land)  he  proceeds  to  consider  the  period 
of  production  for  the  element  of  labor.  If,  he  says,  an  arti- 
cle costs  100  days'  labor,  of  which  20  days  must  be  spent 
10  years  before  the  completion  of  the  article,  20  days 
9  years  before  completion,  and  thereafter  5  days  in  each 
succeeding  year  until  completion,  whereupon  20  days' 
labor  are  spent  in  finishing  touches,  the  production  period 
for  this  article  is  the  average  age  of  these  several  brief 
terms  of  labor;   namely, 

20  X  10  +  20x9+5x8  +  5  x7  +  5x6  +  5x5  +  5x4+5x  3  +  5  x2  +  5x  1  +  20x0     560 

100  ~  100 

or  5.6  years. ^  In  other  words,  all  the  labor  expended  in 
the  production  of  the  article  is  regarded  as  concentrated 
at  one  point  of  time  5.6  years  prior  to  its  completion. 
This  point  is  what  mathematicians  call  the  "center  of 
gravity"  of  the  various  portions  of  labor  expended.  First, 
in  regard  to  the  location  of  this  point,  we  may  ask 
why  the  particular  method  of  averaging  which  Bohm- 
Bawerk  employs  is  assumed  by  him  to  be  the  correct  one. 
His  average  is  a  ''weighted  arithmetical  mean."  There 
are  many  other  possible  methods  of  averaging  any  series 
of  numbers.  The  particular  kind  of  average  chosen  in 
any  special  problem  is  a  matter  of  prime  importance  in 
cases,  like  the  present,  in  which  the  numbers  are  widely 
divergent.  In  cases  in  which  the  numbers  do  not  vary 
widely,  there  is  little  practical  need  of  distinguishing  be- 
tween the  different  methods  of  averaging.  Experience 
with  index  numbers  shows,  for  instance,  that  the  arith- 
metical,  geometrical,   and   harmonical   "means"   and  an 

'  The  Positive  Theory  of  Capital,  English  translation,  London  (Mac- 
millan),  1891,  p.  89. 


Sec.  2]  BOHM-BAWERK'S  THEORY  57 

infinite  number  of  other  "means,"  *  will  agree  very  closely. 
But  where,  as  in  the  present  case,  some  of  the  elements 
averaged  are  very  small  and  others  very  large,  their  means 
will  differ  widely  according  to  the  different  methods  of 
averaging.  Tlius,  in  the  example  used  by  Bohm-Bawerk, 
if  we  apply,  instead  of  the  weighted  arithmetical,  the 
weighted  geometrical  mean,  we  shall  obtain  0  years,^ 
instead  of  5.6  years  as  the  average.  The  weighted  harmoni- 
cal  mean  will  also  be  0. 

But  suppose  the  question  of  the  correct  formulation  of 
the  average  production  period  for  an  individual  article 
to  have  been  satisfactorily  settled,  in  what  manner  is  it 
proposed  to  combine  the  production  periods  of  different 
articles?  Here  are  involved,  considerably  magnified,  all 
the  well-known  difficulties  of  constructing  a  suitable  index- 
number.  Supposing  the  average  production  period  of 
cloth  is  2  years  and  iron  5  years,  how  are  we  to  obtain 
the  average  production  period  for  cloth  and  iron?  No 
one  would  maintain  that  in  such  averaging  between  dif- 
ferent commodities,  they  should  all  be  assumed  as  equally 
important.  They  must  be  weighted.  To  obtain  the  aver- 
age of  2  and  5  for  the  cloth  and  iron,  are  we  to  weight 
these  two  commodities  according  to  the  value  of  the 
amounts  annually  consumed?  If  so,  will  not  the  rate  of 
interest  be  involved  in  the  value  of  the  cloth  and  the  iron  ? 

Again,  Bohm-Bawerk's  theory  of  the  production  period 
requires  us  to  combine  a  number  of  seemingly  discon- 
nected time-elements.     Tlius,  the  "period  of  production" 


*  For  a  mathematical  statement  of  this  topic,  see  Appendix  to 
Chap.  IV,  §  1. 

^  To  be  exact,  not  quite  0  years;  for  it  is  physically  impossible  to 
have  the  last  instalment  of  labor,  namely,  20  days,  all  put  in  at  an 
instant.  Bohm-Bawerk  speaks  of  this  20  days  of  labor  as  immedi- 
lately  preceding  the  finishing  of  the  productive  process.  It,  like  the 
other  elements  of  labor,  is  located  in  the  past,  though  its  remoteness 
from  the  present  is  very  small,  let  us  say  one  day,  or  -j^-j  years.  Then 
the  geometrical  mean  would  be,  not  zero,  but 
^'^^10'^'  X  [}■'■'  X  8^  X  7*  X  «*  X  5*  X  4"  X  3°  X  2*  X  P  X  {^h)'"'  or  1.3  years. 


58  THE  RATE  OF  INTEREST  [Chap.  IV 

of  obtaining  water  from  a  well  is  not,  by  Bohm-Bawerk's 
method  of  estimation,  the  time  consumed  in  merely  send- 
ing down  and  drawing  up  the  bucket.  His  theory  requires 
us  to  add  to  this  interval  of  time  some  fraction  of  the  time 
of  digging  the  well,  and  to  this,  some  fraction  of  the  time 
of  making  the  spade  by  which  the  well  was  dug,  and  then, 
some  fraction  of  the  time  of  making  the  machinery  by 
which  the  spade  was  manufactured,  and  again,  some  frac- 
tion of  the  time  of  constructing  the  tools  by  which  the 
machinery  was  made,  and  so  on,  thus  carrying  our  calcula- 
tions indefinitely  into  the  past.  Waiving  other  objections, 
what  is  to  insure  that  the  items  representing  the  distant 
past  will  be,  as  Bohm-Bawerk  alleges,^  negligible  quantities  ? 
Such  an  assertion  as  to  the  convergence  of  the  mathe- 
matical series  in  question  should  receive  substantiation. 

Professor  Fetter  ^  and  others  ^  have  criticised  Bohm- 
Bawerk's  concept  of  a  production  period  so  fully  that  we 
need  not  mention  additional  perplexities.^ 


§  3 

Passing  over  the  second  step,^  to  which  no  objection  is 
offered,  we  come  to  the  third  and  crucial  step  in  Bohm- 
Bawerk's  theory  of  the  technical  superiority  of  present  goods ; 
namely,  that  the  productiveness  of  long  processes  confers 
a  special  "technical  advantage"  to  the  possessor  of  present 
goods  or  labor.  This  advantage  produces,  so  Bohm-Bawerk 
believes,  a  preference  for  present  over  future  goods  which 
is  entirely  apart  from  and  in  addition  to  the  preference 
due  to  the   perspective  underestimate  of  the  future  or 

*  The  Positive  Theory  of  Capital,  p.  88. 

*  See  "The  Roundabout  Process  in  the  Interest  Theory,"  by  F.  A. 
Fetter,  Quarterly  Journal  of  Economics,  Vol.  XVII  (November,  1902), 
p.  13  passim.     Cf.  Taussig,  Wages  and  Capital,  p.  12. 

'  See  Lexis,  Jahrbuch  fiir  Gesetzgebung,  Verwaltung  und  Volks- 
wirtschaft,  1895,  pp.  332-337;    Bortkiewicz,  ibid.,  1906,  p.  69. 

*  See,  however.  Appendix  to  Chap.  IV,  §  2. 
'  See  Appendix  to  Chap.  IV,  §  3. 


Sec.  3] 


BOHM-BAWERK'S  THEORY 


59 


that  due  to  the  underendowment  of  the  present.  Grant- 
ing for  the  moment  the  vahdity  of  the  concept  of  a  pro- 
duction period,  and  that  the  longer  the  period,  the  greater 
its  product,  it  may  still  be  shown  that  no  such  "technical 
superiority"  follows.  Since  Bohm-Bawerk  regards  this 
part  of  his  theory  as  the  most  essential  of  all,  and  repeat- 
edly states  that  the  theory  must  stand  or  fall  by  the  truth 
or  falsity  of  that  part,  it  becomes  necessary  to  examine  his 
claim  in  considerable  detail. 

Bohm-Bawerk  supports  his  assertion  of  the  existence  of 
a  "technical  superiority"  ^  by  elaborate  illustrative  tables, 
reproduced  below:  — 

A  MONTH'S  LABOR  AVAILABLE   IN   1888  YIELDS 


For  the 
Economic  Period 

Units  of 
Product 

True  Marginal 
Utility  of  Unit 

Marginal 
Utility  Reduced 
in  Perspective 

Amount  of 

Value  of  Entire 

Product 

1888 

100 

5 

5 

500 

1889 

200 

4 

3.8 

760 

1890 

280 

3.3 

3 

840 

1891 

350 

2.5 

2.2 

770 

1892 

400 

2.2 

2 

800 

1893 

440 

2.1 

1.8 

792 

1894 

470 

2 

1.5 

705 

1895 

500 

1.5 

1 

500 

A  MONTH'S  LABOR   AVAILABLE   IN   1889  YIELDS 


For 
Economic  Period 

Units 

True  Marginal 
Utility 

Reduced 

Marginal 

Utility 

Value 

1888 
1889 
1890 
1891 
1892 
1893 
1894 
1895 

100 
200 
280 
350 
400 
440 
470 

5 

4 

3.3 

2.5 

2.2 

2.1 

2 

1.5 

5 

3.8 

3 

2.2 

2 

1.8 

1.5 

1 

380 
600 
616 
700 
720 

660 
470 

»  The  Positive  Theory  of  Capital,  p.  266. 


60 


THE  RATE  OF  INTEREST 


[Chap.  IV 


A  MONTH'S  LABOR  AVAILABLE   IN   1890  YIELDS 


For 
Economic  Period 

Units 

True  Marginal 

Utility 

Reduced 

Marginal 

Utility 

Value 

1888 

5 

5 

1889 



4 

3.8 

1890 

100 

3.3 

3 

300 

1891 

200 

2.5 

2.2 

440 

1892 

280 

2.2 

2 

560 

1893 

350 

2.1 

1.8 

630 

1894 

400 

2 

1.5 

600 

1895 

440 

1.5 

1 

440 

A  MONTH'S  LABOR  AVAILABLE  IN  1891  YIELDS 


For 
Economic  Period 

Units 

True  Marginal 
Utility 

Reduced 

Marginal 

Utility 

Value 

1888 

5 

5 

1889 

4 

3.8 

1890 



3.3 

3 

1891 

100 

2.5 

2.2 

220 

1892 

200 

2.2 

2 

400 

1893 

280 

2.1 

1.8 

504 

1894 

350 

2 

1.5 

525 

1895 

400 

1.5 

1 

400 

Beginning  with  the  first  table  we  see  that  it  represents, 
in  the  second  column,  the  units  of  product  obtainable 
in  various  years  through  the  investment  of  a  month's 
labor  in  1888.  Thus,  a  month's  labor  in  1888  may  be  in- 
vested so  as  to  produce  280  miits  in  the  year  1890,  or  470 
units  in  the  year  1894. 

The  third  column  gives  the  marginal  utility  of  the  prod- 
uct to  the  investor  in  the  various  years.  This  column  is 
formed  on  the  assumption  that  the  individual  is  in  "grad- 
ually improving  circumstances,"  so  that  in  1895  a  unit 
of  product  will  be  estimated  in  his  mind  at  1.5  units  of 
utiUty,  whereas  in  1888  the  same  imit  would  have  been 
estimated  at  5. 


Sec.  4]  BOHM-BAWERK'S  THEORY  61 

The  fourth  column  shows  the  present  vakiation  of  the 
aforesaid  marginal  utilities.  Thus,  the  imit  of  product 
in  1895,  while  worth  1.5  units  of  utility  at  that  date,  is, 
when  foreseen  in  perspective,  worth  only  1. 

The  fifth  column  shows  the  (subjective)  value  of  the 
product.  This  is  obtained  by  multiplying  the  number  of 
units  of  product  by  the  reduced  marginal  utility ;  that  is, 
multiplying  the  items  in  the  second  column  by  the  cor- 
responding items  in  the  fourth  column. 

Beginning  with  the  first  table,  Bohm-Bawerk  selects  the 
maximum  figm'e  (underscored)  in  the  last  column.  This 
maximum  signifies  that  a  month's  labor  available  in  1888 
would  best  be  invested  so  as  to  mature  in  1890,  because  the 
present  value  of  the  product  attainable  in  1890,  but  reck- 
oned in  1888,  is  the  maximum,  840,  of  all  the  present 
values.  In  the  same  way  it  is  seen  from  the  second  table 
that  a  month's  labor  available  in  1889  will  be  so  invested 
as  to  mature  in  1893;  for,  when  thus  invested,  it  has  its 
maximum  present  value  (reckoned  in  1888).  But  this 
maximum  present  value  is  only  720,  which  is  less  than  the 
previous  maximum  present  value  of  the  product  (840)  if 
the  labor  were  invested  in  1888.  Tliere  is,  therefore,  says 
Bohm-Bawerk,  a  "technical  advantage"  in  having  the 
labor  available  in  1888  over  having  it  available  only  in 
1889.  In  the  same  way,  it  is  still  less  advantageous  to 
have  a  month's  labor  available  in  1890,  as  the  product  is 
in  that  case  worth  only  630  in  the  present  (1888).  Like- 
wise, a  month's  labor  available  in  1891  is  still  less  valuable, 
having  a  value  (in  1888)  of  only  525.  Thus  we  see  that 
the  longer  the  labor  is  deferred  the  less  the  value  of  its 
best  product,  as  reckoned  in  the  present  (1888). 


§  4 

The  result  is  correct ;  but  Bohm-Bawerk  is  mistaken  in 
ascribing  any  part  of  the  result  to  the  fact  that  the  longer 


62  THE  RATE  OF  INTEREST  [Chap.  IV 

processes  are  the  more  productive.  In  his  tables  he 
assumes  the  existence  of  one  or  both  of  the  other  two 
factors,  —  the  relative  overprovision  for  the  future  as 
compared  with  the  present,  and  the  perspective  under- 
valuation of  the  future,  due  to  lack  of  intellectual  imagi- 
nation and  of  self-control.  Examination  will  show  that 
it  is  these  elements,  and  these  alone,  which  produce  the 
advantage  of  present  over  future  goods  which  the  tables 
display. 

Bohm-Bawerk  has  curiously  deluded  himself,  as  well  as 
many  of  his  followers,  on  this  point.     He  says :  ^  — 

"I  repeat  emphatically  that  this  result  is  not  an  accidental  one, 
such  as  might  have  made  its  appearance  in  consequence  of  the  par- 
ticular figures  used  in  our  hypothesis.  On  the  single  assumption 
that  longer  methods  of  production  lead  generally  to  a  greater  out- 
put, it  is  a  necessary  result ;  a  result  which  must  have  occurred, 
in  an  exactly  similar  way,  whatever  might  have  been  the  figures 
of  quantity  of  product  and  value  of  unit  in  the  different  years." 

As  a  matter  of  fact,  however,  the  result  does  not  at  all 
follow  from  "the  single  assumption  that  longer  methods 
of  production  lead  generally  to  a  greater  output."  It 
has  nothing  whatever  to  do  with  that  assumption.  In 
other  words,  it  has  nothing  to  do  with  the  fact  that  the 
series  of  numbers  in  the  second  column  of  the  tables  in- 
creases, but  with  the  fact  that  the  series  of  nmnbers  in  the 
fourth  column  decreases. 

If  we  should  make  the  opposite  assumption  from  that 
of  Bohm-Bawerk,  namely,  that  the  longer  the  productive 
process  the  smaller  will  be  the  return,  the  very  same  result 
would  follow.  The  labor  would  still  be  invested  at  the 
earliest  possible  moment.  Let  the  figures  in  the  second 
column  decrease  instead  of  increase;  the  only  difference 
would  be  that  the  month's  labor  available  in  1888  would 
now  be  so  invested  as  to  bring  immediate  returns  instead 

1  The  Positive  Theory  of  Capital,  p.  268. 


Sec.  4]  BOHM-BAWERK'S  THEORY  63 

of  being  invested  in  a  two  years'  process  as  before.  The 
present  value,  in  1888,  of  the  investment  of  the  month's 
labor  of  that  year  in  an  immediately  returning  process 
would  be,  as  before,  the  product  of  100  by  the  marginal 
utility,  5,  or  500,  whereas  if  the  labor  were  invested  for  a 
year  the  present  value  would  be  less;  for  its  amount  is 
found,  as  before,  by  multiplying  the  number  of  units  of 
product  (now  assumed  less  than  100)  by  the  marginal 
utility  (which  is  less  than  5).  Likewise,  the  month's  labor 
available  in  1889  would  also  be  invested  so  as  to  yield  an 
immediate  return  and  would  possess  a  value  of  100  x  3.8, 
or  380.  If  similar  calculations  are  performed  for  each  year 
and  the  results  are  compared,  it  will  appear  that  the  invest- 
ment in  1888  yields  the  highest  return,  just  as  it  did  on  the 
previous  hypothesis. 

Again,  the  same  result  would  follow  if  the  productivity 
increased  and  then  decreased  in  all  the  tables,  as  follows: 
100,  200,  230,  200, 100,  etc.  For  examination  will  show  that 
the  labor  available  in  1888  would  have  a  maximum  value  of 
200  X  3.8,  or  760 ;  that  available  in  1889,  a  value  of  200  x  3, 
or  600 ;  that  in  1890,  a  value  of  230  x  2,  or  460 ;  that  of  1891, 
230  X  1.8,  or  414,  etc.  These  results,  760,  600,  460,  414,  etc., 
constitute  a  descending  series,  and  show  again  the  greater 
desirability  of  labor  which  is  available  early  as  compared 
with  labor  which  is  available  late.  It  is  just  as  easy  to 
show  that  if  the  productivity  first  decreases  and  then  in- 
creases, the  same  advantage  of  present  over  future  labor 
wiU  result. 

Such  illustrative  figures  could  be  reproduced  indefi- 
nitely. The  reader  can  readily  convince  himself  by  trial 
that  as  long  as  the  column  of  "reduced  marginal  utility" 
decreases,  the  column  of  "units  of  product"  may  be  of 
any  description  whatever,  without  in  the  least  affecting 
the  essential  result  that  the  earlier  the  month's  labor  is 
available,  the  higher  is  its  value. ^ 

*  For  a  mathematical  proof,  see  Appendix  to  Chap.  IV,  §  4. 


64 


THE  RATE  OF  INTEREST 


[Chap.  IV 


§    5 

On  the  other  hand,  if  the  conditions  are  reversed  and 
the  fourth  column  of  "reduced  marginal  utility"  does  not 
decrease,  the  earlier  available  labor  will  not  have  a  higher 
value,  whatever  may  be  the  character  of  the  second  column 
of  "units  of  product." 

Bohm-Bawerk,  however,  specifically  denies  this :  ^  — 

"The  sujjeriority  in  value  of  present  means  of  production,  which 
is  based  on  their  technical  superiority,  is  not  one  borrowed  from 
these  circumstances  [i.e.,  the  perspective  underestimate  of  the  future 
and  the  relative  underendowment  of  the  present]  ;  it  would  emerge 
of  its  own  strength  even  if  these  were  not  active  at  all.  I  have 
introduced  the  two  circumstances  into  the  hypothesis  only  to  make 
it  a  little  more  true  to  life,  or,  rather,  to  keep  it  from  being  quite 
absurd.  Take,  for  instance,  the  influence  of  the  reduction  due  to 
perspective  entirely  out  of  the  illustration,  and  we  get  the  follow- 
ing figures:  — 

A  MONTH'S  LABOR  OF  THE  YEAR 


1888 

1889 

1890 

1891 

1888 

500 

Ss 

1889 

800 

400 

FOR    T 

c  Per 

1890 

924 

660 

330 

< 

1891 

875 

700 

500 

250 

■  fu 

1892 

880 

770 

616 

440 

o 
2 

►J  ° 
«  o 

1893 
1894 

924 
940 

840 
880 

735 

800 

588 
700 

H 

s 
^ 

[         1895 

750 

705 

660 

600   J 

It  is,  as  Bohm-Bawerk  remarks,  still  true  that  the  month's 
labor  available  in  1888  is  more  highly  valued  than  the  same 
month's  labor  available  at  a  later  date.  But  he  has  care- 
fully retained  in  his  illustration  one  of  the  "two  circum- 
stances "  which  he  stated  could  be  discarded ;  namely,  the 


The  Positive  Theory  of  Capital,  p.  268. 


Sec.  5]  BOHM-BAWERK'S  THEORY  65 

relative  overprovision  for  the  future.  To  leave  one  of  these 
two  circumstances  effective  instead  of  both  is  merely  to 
change  slightly  the  series  in  the  fourth  column  of  the  pre- 
vious tables;  namely,  to  change  it  from  the  descending 
series,  5,  3.8,  3,  2.2,  2,  1.8,  1.5,  1,  to  another  descending 
series,  5,  4,  3.3,  2.5,  2.2,  2.1,  2,  1.5.  The  change  in  the  par- 
ticular numbers  is  quite  immaterial  as  long  as  the  series  is 
still  descending.  It  does  not  matter  whether  the  descent  is 
due  to  perspective,  or  to  the  relative  overprovision  for  the 
future,  or  to  both.  Tlie  essential  fact  is  that  the  numbers 
in  the  fourth  column  still  constitute  a  descending  series. 
The  only  fair  test  of  the  independence  of  Bohm-Bawerk's 
third  factor  —  the  alleged  technical  superiority  of  present 
over  future  goods  —  would  be  to  strike  out  both  the  other 
elements  (underestimate  and  overprovision  of  the  future) 
so  that  there  should  be  no  progressive  decrease  in  mar- 
ginal utilities;  in  other  words,  to  make  the  numbers  in 
the  fourth  column  all  equal.  Bohm-Bawerk,  for  some 
reason,  hesitates  to  do  this.     He  says:^  — 

"But  if  we  were  also  to  abstract  the  difference  in  the  circum- 
stances of  provision  in  different  periods  of  time,  the  situation  would 
receive  tlie  stamp  of  extreme  improbability,  even  of  self-contra- 
diction." 

This  is  very  true  indeed ;  for  to  abstract  both  the  under- 
estimate of  the  future  and  underprovision  for  the  present 
is  to  abstract  the  whole  basis  for  interest  and  not  a  part 
merely.  Yet  this  is  no  reason  for  refusing  to  push  the 
inquiry  to  its  limit.  The  consideration  of  this  extreme 
case  will  in  fact  show  clearly  the  error  of  Bohm-Bawerk ; 
for  although  we  shall  have  abstracted  all  true  foundation 
for  interest,  there  will  be  left  what  Bohm-Bawerk  wrongly 
imagines  to  Ije  a  basis  of  interest.  Let  us,  therefore, 
make  all  the  factors  in  the  "reduced  utility"  column  alike, 
say  5.  The  tables  for  1888  and  1889,  condensed,  would 
then  read  as  follows :  — 

'  Ibid.,  p.  269. 


66 


THE  RATE  OF  INTEREST 


[Chap.  IV 


A  MONTH'S  LABOR  AVAILABLE 


IN 

1888  YIELDS 

IN  1889  YIELDS 

For 

Economic 

Units  of 

Reduced 

Value 

Units  of 

Reduced 

Period 

Product 

Utility 

Product 

Utility 

100 

5 

500 

5 

1888 

1889 

200 

5 

1000 

100 

5 

500 

1890 

280 

5 

1400 

200 

5 

1000 

1891 

350 

5 

1750 

280 

5 

1400 

1892 

400 

5 

2000 

350 

5 

1750 

1893 

440 

5 

2200 

400 

5 

2000 

1894 

470 

5 

2350 

440 

5 

2200 

1895 

500 

5 

2500 

470 

5 

2350 
2500 

The  figures  in  the  value  columns  for  1888  and  1889  are 
here  absolutely  alike ;  hence  the  maximum  of  the  former, 
if  there  be  a  maximum,  must  be  identical  with  the  maxi- 
mum of  the  latter. 

Though  Bohm-Bawerk  did  not  consider  this  case  in  his 
tables,  he  speaks  of  it  briefly  in  his  text,  but  seems  to  be 
somewhat  puzzled  by  it.    He  says :  *  — 

"  If  the  value  of  the  unit  of  product  were  to  be  the  same  in  all 
periods  of  time,  however  remote,  the  most  abundant  product  would, 
naturally,  at  the  same  time  be  the  most  valuable.  But  since  the 
most  abundant  product  is  obtained  by  the  most  lengthy  and  round- 
about methods  of  production,  —  perhaps  extending  over  decades 
of  years,  —  the  economic  center  of  gravity,  for  all  present  means 
of  production,  would,  on  this  assimiption,  be  found  at  extremely 
remote  periods  of  time  —  which  is  entirely  contrary  to  all  experi- 
ence." 

Bohm-Bawerk's  confusion  here  is  probably  to  be  ascribed 
to  his  insistence  on  the  indefinite  increase  of  product  with 


Ibid.,  p.  269. 


Sec.  5]  BOHM-BAWERK'S  THEORY  67 

a  lengthening  of  the  production  period.  Had  he  admitted 
into  his  possibihties  the  particular  possibility  that  the  prod- 
uct would  ultimately  decrease  with  a  lengthening  of  that 
period,  the  error  which  he  had  committed  would  have  made 
itself  too  evident  to  escape  his  notice.  As  it  was,  he  found 
himself  dealing  with  an  infinite  series;  and  as  the  history 
of  mathematics  shows,  it  is  not  easy  in  such  inquiries  to 
keep  clear  of  pitfalls.  Yet  even  in  the  hypothesis  of  a  law 
of  indefinite  increase  in  returns  with  increased  length  of 
productive  period,  the  error,  though  concealed,  exists  and 
may  be  shown. 

In  order  not  to  tamper  prematurely  with  any  of  Bohm- 
Bawerk's  hypotheses,  let  us  then  still  assume  this  law  of  in- 
definite increase  of  value  proportionately  with  the  length  of 
the  productive  process.  The  result  of  such  a  fact  would  be 
simply  that  productive  processes  indefinitely  long  would  be 
chosen  by  investors.  The  possessor  of  a  month's  labor, 
whether  available  in  1888  or  1889,  would  invest  it  in  an 
infinite  production  process,  —  a  result  extremely  fantastic, 
but  involved  in  the  hypothesis.  We  need  not  assume  that 
the  product  of  an  infinite  production  period  is  itself  infinite. 
The  increasing  product  may  approach  a  definite  limit. 
This  ought,  in  fact,  to  be  assumed ;  for  we  could  not  imag- 
ine that  a  finite  earth  would  have  an  infinite  product. 
To  fix  our  ideas,  let  us  suppose  that  with  each  year  after 
1895,  with  which  Bohm-Bawerk  breaks  off  his  table,  the 
product  leaps  up  halfway  toward  1000  units.  Thus, 
in  1896  the  product  rises  to  750,  a  rise  of  half  the  interval 
between  500  units  (the  product  of  1895)  and  1000  units. 
In  1897  it  becomes,  in  like  manner,  875,  in  1898,  937.5, 
etc.  The  limit  of  such  a  series  is  1000  units.  A  month's 
labor,  whether  available  in  1888  or  1889,  will  now  have 
the  same  maximum  value,  exactly  1000,  and  there  will 
be  no  "  technical  superiority"  in  present  over  future  goods 
whatever. 

It  is  noteworthy  that  in  treating  this  case  Bohm-Bawerk 
shifts  his  ground.    For  the  case  of  undiminished  marginal 


68  THE  RATE  OF  INTEREST  [Chap.  IV 

utilities,  the  only  comparison  which  he  makes  between  the 
two  series  (that  for  1888  and  that  for  1889)  is  not  a  com- 
parison between  their  maxima,  such  as  he  made  in  his 
previous  cases,  but  a  comparison  between  individual  terms. 
He  states  in  a  footnote :  ^  — 

"...  The  month's  labour  of  1888  remains  superior  to  that  of 
1889.  For,  as  regards  any  one  remote  period,  say,  the  year  1988, 
the  former,  as  employed  in  a  process  longer  by  one  year,  could  pro- 
duce a  somewhat  greater  product  than  the  latter." 

Such  an  individual  comparison  is,  of  course,  beside  the 
point ;  but  granted  that  it  should  be  made  at  all,  why  is  it 
made  between  two  items  relating  to  the  same  calendar 
year?  Why  not  make  it  between  two  items  relating  to 
the  same  production  period  ?  Why  conclude  that  a  month's 
labor  of  1888  is  superior  to  that  of  1889  because,  say  in 
1892,  the  first  yields  400,  whereas  the  second  yields  only 
350,  rather  than  conclude  that  they  are  equal,  since,  in 
a  four  years'  process,  the  labor  of  1888  yields  400,  and 
that  of  1889  yields  also  400  ?  Tliat  the  fruition  is  deferred 
one  year  in  the  latter  case  is  no  disadvantage  under  the 
present  hypothesis,  for  we  have  expressly  eliminated  from 
consideration  any  overprovision  or  underestimation  of 
the  future;  it  becomes  a  matter  of  entire  indifference 
whether  the  400  is  obtained  m  1892  or  1893.' 


§  6 

Thus  far  we  have  not  altered  any  of  Bohm-Bawerk's 
hypotheses;   but  if  we  allow  ourselves  to  assume,  as  prac- 


»  Ihid.,  p.  269. 

*  Cf .  Bortkiewicz,  "  Der  Kardinalfehler  der  Bohm-Bawerkschen 
Zinstheorie,"  Jahrbuch  fiir  Gesetzgebung,  Verwaltung  und  Volkswirt- 
achaft,  1906,  pp.  71-73. 


Sec.  6] 


BOHM-BAWERK'S  THEORY 


69 


tically  we  ought  to  assume,  that  sometime  the  product 
decreases,  no  matter  for  how  long  a  production  period,  we 
shall  have  a  more  practical  illustration  of  the  fact  that  the 
labor  available  in  1888  and  that  available  in  1889  stand 
on  a  perfect  equality. 

Let  us  assume  that  Bohm-Bawerk's  table  of  products 
holds  true  as  far  as  he  carries  it,  1895,  but  that  thereafter 
the  numbers  decrease,  as  in  the  next  table.  In  this  table 
are  also  given  the  products  of  a  month's  labor  available 
in  1889  and  other  years :  — 


PRODUCT   OF  A  MONTH'S   LABOR  AVAILABLE  IN 


For  the 

Economic 

Period 

1888 

1889 

1890 

1891 

1892 

1888 

100 



1889 

200 

100 

1890 

280 

200 

100 

1891 

350 

280 

200 

100 

1892 

400 

350 

280 

200 

100 

1893 
1894 
1895 

440 
470 
500 

400 
440 
470 

350 
400 
440 

280 
350 
400 

200 
280 
350 

Units  of 
Product 

1896 

490 

500 

470 

440 

400 

1897 

480 

490 

500 

470 

440 

1898 

460 

480 

490 

500 

470 

1899 

430 

460 

480 

490 

500 

1900 

410 

430 

460 

480 

490   J 

If,  as  before,  we  suspend  the  operation  of  the  two 
"circumstances  "  (overprovision  and  underestimation  of 
future)  and  employ  for  the  "reduced  utility"  the  constant 
number,  5,  we  have  the  following  table  for  the  "value" 
columns :  — 


70 


THE  RATE  OF  INTEREST  [Chap.  IV 

A   MONTH'S   LABOR  AVAILABLE  IN 


Yields  in 

Value  for 
THE  Economic 

1888 

1889 

1890 

1891 

1892 

Period 

1888 

500 

^ 

1889 

1000 

500 

1890 

1400 

1000 

500 

1891 

1750 

1400 

1000 

500 

1892 

2000 

1750 

1400 

1000 

500 

1893 

2200 

2000 

1750 

1400 

1000 

1894 

2350 

2200 

2000 

1750 

1400 

Valub 

1895 

2500 

2350 

2200 

2000 

1750 

1896 

2450 

2500 

2350 

2200 

2000 

1897 

2400 

2450 

2500 

2350 

2200 

1898 

2300 

2400 

2450 

2500 

2350 

1899 

2150 

2300 

2400 

2450 

2500 

1900 

2050 

2150 

2300 

2400 

2450 

This  table  of  values  is  simply  the  previous  table  of  prod- 
ucts magnified  fivefold,  and  is  only  given  separately  lest 
there  be  any  possible  room  for  doubt  that  the  reasoning 
applies  to  "value "  as  well  as  to  " product."  We  see  clearly 
that  the  labor  of  1888  will  be  invested  in  a  seven-year 
productive  process  maturing  in  1895,  and  having  a  present 
value,  reckoned  in  1888,  of  2500  imits  of  value;  that  the 
labor  of  1889  wiU  likewise  be  put  into  a  seven-year  pro- 
ductive process,  maturing  in  1896,  and  having  a  present 
value  in  1888  of  2500.  Similarly,  the  labor  of  each  succeed- 
ing year  matures  seven  years  later,  but  is  worth  to-day 
(1888)  its  full  value  of  2500. 

Our  conclusion  is  that  if  we  eliminate  the  "other  two 
circumstances "  (relative  underestimate  of,  and  over- 
provision  for,  the  future),  we  eliminate  entirely  the  supe- 
riority of  present  over  future  goods,  and  the  supposed 
third  circumstance  of  "technical  superiority"  therefore 
turns  out  to  be  non-existent. 

The  fact   is   that  the  only  reason  any  one   can  prefer 


Sec.  7]  BOHM-BAWERK'S  THEORY  71 

the  product  of  a  month's  labor  invested  to-day  to  the 
product  of  a  month's  labor  invested  next  year  is  that 
to-day's  investment  will  mature  earlier  than  next  year's  in- 
vestment. If  a  fruit  tree  is  planted  to-day  which  will  bear 
fruit  in  four  years,  the  labor  available  to-day  for  plant- 
ing it  is  preferred  rather  than  the  same  amoimt  of  labor 
available  next  year;  because,  if  the  planting  is  deferred 
until  next  year,  the  fruit  will  likewise  be  deferred  a  year, 
maturing  in  five  instead  of  four  years  from  the  present. 
It  does  not  alter  this  essential  fact  to  speak  of  the  possi- 
bility of  a  number  of  different  investments,  A  month's 
labor  to-day  may,  it  is  true,  be  spent  in.  planting  slow- 
growing  or  fast-growing  trees;  but  so  may  a  month's 
labor  invested  next  year.  It  is  from  the  preference  for 
the  early  over  the  late  fruition  of  any  productive  process 
that  the  so-called  "technical  superiority  of  present  over 
future  goods"  derives  all  its  force.  The  imagined  "third 
circumstance"  producing  a  superiority  in  present  goods 
is  only  the  first  two  circumstances  in  disguise. 


§  7 

But  our  distinguished  author  attempts  to  prove  that  his 
third  circumstance"  —  the  alleged  technical  superiority 
of  present  goods  —  is  really  independent  of  the  first  two, 
by  the  following  reasoning :  ^  — 


(( 


"...  If  every  employment  of  goods  for  future  periods  is,  not 
only  technically,  but  economically,  more  remunerative  than  the 
employment  of  them  for  the  present  or  near  future,  of  course  men 
would  withdraw  their  stocks  of  goods,  to  a  great  extent,  from  the 
service  of  the  present,  and  direct  them  to  the  more  remunerative 
service  of  the  future.  But  this  would  immediately  cause  an  ebb- 
tide in  the  provision  for  the  present,  and  a  flood  in  the  provision 
for  the  future,  for  the  future  would  then  have  the  double  advantage 
of  having  a  greater  amount  of  productive  instruments  directed  to 

»  Ihid.,  pp.  269,  270. 


72  THE  RATE  OF  INTEREST  [Chap.  IV 

its  service,  and  those  instruments  employed  in  more  fruitful  meth- 
ods of  production.  Thus  the  difference  in  the  circumstances  of 
provision,  which  might  have  disappeared  for  the  moment,  would 
recur  of  its  own  accord. 

"But  it  is  just  at  this  point  that  we  get  the  best  proof  that  the 
superiority  in  question  is  independent  of  differences  in  the  circum- 
stances of  provision :  so  far  from  being  obliged  to  borrow  its  strength 
and  activity  from  any  such  difference,  it  is,  on  the  contrary,  able, 
if  need  be,  to  call  forth  this  very  difference  .  .  .  We  have  to  deal 
with  a  third  cause  of  the  surplus  value,  and  one  which  is  independ- 
ent of  any  of  the  two  already  mentioned." 

The  argument  here  is  that  if  "the  other  two  circum- 
stances" which  produce  interest,  namely,  underestimate 
of  the  future  and  underendowment  of  the  present,  are  tem- 
porarily absent,  they  will  be  forced  back  into  existence  by 
the  choice  of  roundabout  processes.  In  other  words,  the 
"technical  superiority  of  present  goods"  produces  interest 
by  restoring  the  "other  two  circumstances."  But  this  is 
tantamount  to  the  admission  that  "technical  superiority" 
actually  depends  for  its  force  on  these  "other  two  circum- 
stances" and  is  not  "independent."  The  essential  fact  is 
that  its  presence  does  not  produce  interest  when  the  other 
two  are  absent.  In  short,  the  " technical  superiority"  of 
present  goods  is  a  delusion,^  and  the  only  way  in  which  the 
existence  of  long  processes  of  production  acts  on  interest 
is  by  overendowmg  the  future  and  underendowing  the 
present,  thus  creating  a  "scarcity  value"  of  present  goods. 

Since  the  foregoing  criticism  on  Bohm-Bawerk's  theory  of 
the  technical  superiority  of  present  over  future  goods  was  first 
written,  very  similar  criticism  has  been  made  by  Adolphe 
Landry^  and  by  Ladislas  von  Bortkiewicz.^  So  far  as 
the  writer  knows,  Landry  is  the  first  to  have  set  forth 
clearly   and   definitely    the   fallacy   contained   in    Bohm- 

*  Cf.  Bortkiewicz,  "Der  Kardinalfehler  der  Bohm-Bawerkschen 
Zinstheorie,"  Jahrbuch  fi'ir  Gesetzgebung,  Vcrwaltung  und  Volkswirt- 
schaft,  1906,  pp.  61-90. 

^  L'InterH  du  Capital. 

2  Loc.  cit.,  pp.  61-00. 


Sec.  7]  BOHM-BAWERK'S  THEORY  73 

Bawerk's  theory  of  "technical  superiority."  Every  reader 
of  Bohm-Bawerk,  however,  must  have  felt  dissatisfied 
with  his  explanations;  and  sundry  expressions  of  Bohm- 
Bawerk's  suggest  that  he  was  dissatisfied  himself.  His 
theory  of  technical  superiority  stands  out  as  incongruous 
with  the  rest  of  his  work,  and  is  more  in  keeping  with 
the  productivity  theories  which  he  has  done  so  much  to 
demolish.  It  would  seem  as  though,  like  a  successful 
warrior,  he  had  been  haunted  by  the  ghosts  of  his  slain 
enemies.    As  Professor  Fetter  has  said  : '  — 

"It  has  been  a  surprise  to  many  students  of  Bohm-Bawerk  to 
find  that  he  has  presented  a  theory,  the  most  prominent  feature 
of  which  is  the  technical  iDroductiveness  of  roundabout  processes . 
His  criticism  of  the  productivity  theories  of  interest  has  been  of 
such  a  nature  as  to  lead  to  the  belief  that  he  utterly  rejected  them. 
But  evidently  such  is  not  the  case.  Critics  have  pretty  generally 
agreed  that  the  theory  of  the  roundabout  process  is  a  productivity 
theory  of  interest." 

It  is,  therefore,  somewhat  strange  to  find  Bohm-Bawerk 
strenuously  insisting  on  the  importance  of  his  "technical" 
theory.     He  writes :  ^  — 

"The  statement  of  how  the  productivity  of  capital  works  into 
and  together  with  the  other  two  grounds  of  the  higher  valuation 
of  present  goods,  I  consider  one  of  the  most  difficult  points  in  the 
theory  of  interest,  and,  at  the  same  time,  the  one  which  must  decide 
the  fate  of  that  theory.  It  is  just  at  this  point  that  we  discover 
the  chief  weakness  in  Jevons's  otherwise  suggestive  work.  None 
of  the  groups  of  phenomena  concerned  escaped  his  keen  observa- 
tion; what  did  escape  him  was  the  way  in  which  they  work  into 
one  another." 

And,  referring  to  Launhardt,  he  says :  ^  — 

"  But,  on  the  other  hand,  it  is  a  sensible  omission  that  the  differ- 
ence between  the  values  of  present  and  future  goods  is  traced 

•  "The  'Roundabout  Process'  in  the  Interest  Theory,"  by  Frank 
A.  Fetter,  Quarterly  Journal  of  Economics,  Vol.  XVII,  November, 
1902. 

^  The  Positive  Theory  of  Capital,  p.  277,  footnote. 

»  Ibid.,  p.  278. 


74  THE  RATE  OF  INTEREST  [Chap.  IV 

exclusively  to  this  factor,  and  that  the  much  more  important 
factor  that  cooperates  with  it,  that  of  the  greater  productiveness, 
does  not  get  even  the  scanty  consideration  it  gets  from  Jevons," 

Before  leaving  the  subject,  justice  requires  that  we  should 
dissent  from  Bohm-Bawerk's  opinion  that  he  has  made 
no  substantial  contribution  to  the  theory  of  interest  aside 
from  his  particular  "technical"  feature.  His  work  in 
historical  criticism  is  a  model  both  for  the  historian  and 
for  the  critical  analyst,  and  his  enunciation  of  the  agio 
theory,  while  partially  anticipated  by  Jevons,  Sax,  and 
Launhardt,  was  so  much  more  clearly  and  perfectly  worked 
out  that  it  gains  an  almost  independent  form  in  his 
hands.  Tlie  only  writer  who  has  equaled  Bohm-Bawerk 
was  one  with  whom  the  latter  was  not  acquainted,  namely, 
John  Rae.  His  valuable  contribution  to  the  subject  was, 
through  a  curious  chain  of  circumstances,  lost  to  two 
generations  of  readers,  and  has  only  recently  been  revived 
and  made  accessible  through  Professor  Mixter. 

If  we  cast  out  from  the  agio  theory  Bohm-Bawerk's 
special  feature,  his  alleged  "technical  superiority  of  present 
goods,"  the  theory  which  remains  is  believed  to  be  correct. 
It  is,  however,  still  incomplete,  for  there  remains  the  gap 
which  Bohm-Bawerk  sought  to  fill,  —  the  formulation  of 
the  exact  manner  in  which  the  "technique"  or  actual  con- 
ditions of  production  enter  into  the  determination  of 
interest.  In  Part  III  we  shall  attempt  to  supply  this 
deficiency. 


PART   II.     First  Approximation 

Chapter      V.  Appkeciation  and  Interest 

Chapter    VI.  Time-Preference 

Chapter  VII.  First   Approximation  to  the  Theory 

OF  Interest  (assuming  income  rigid) 


CHAPTER  V 

APPRECIATION   AND   INTEREST 
§1 

In  the  four  preceding  chapters  we  have  criticised  those 
theories  of  interest  which  enjoy  the  greatest  currency  in 
present  economic  and  business  circles.  Inasmuch  as  we 
have  found  radical  defects  in  all  of  them,  our  best  course 
now  is  to  formulate  de  novo  what  seems  to  us  to  be  the  cor- 
rect theory.  At  the  outset  we  need  to  note  an  oversight 
common  to  all  the  theories  reviewed.  In  none  of  them  is 
any  account  taken  of  the  fact  that  the  number  expressing 
the  rate  of  interest  depends  upon  the  monetary  standard 
of  value  in  terms  of  which  that  rate  of  interest  is  expressed. 
To  say  that  the  rate  of  interest  is  4  per  cent,  means  ^  that 
the  quantity  of  this  year's  goods  which  is  worth  $100  is 
equivalent  to  the  quantity  of  next  year's  goods  which  is 
worth  $104.  In  this  statement  we  observe  that  the 
"  goods  "  which  are  considered  are  expressed  not  in  their  own 
special  units,  —  pounds,  bushels,  yards,  etc.,  —  but  in  terms 
of  a  standard  of  value.  The  standard  of  value  chosen  is 
usually  money.  This  money,  the  $100  and  $104,  is  nomi- 
nally exchanged;  but  actually  it  merely  measures  the 
"goods"  which  are  exchanged.  When  a  man  lends  $100 
this  year  in  order  to  obtain  $104  next  year,  he  is  really 
sacrificing  not  one  hundred  dollars  in  money,  but  one  hun- 
dred dollars'  worth  of  goods  such  as  food,  clothing,  books, 
or  pleasure  trips,  in  order  to  obtain  next  year  not  one 
hundred  and  four  dollars  in  money,  but  one  hundred  and 
four  dollars'  worth  of  other  goods  which  he  desires. 

*  See  Glossary  at  end  of  this  volume  ;  also  the  writer's  The  Nature 
of  Capital  and  Income  (Chap.  XI),  tte  nomenclature  of  which  book  is 
followed  in  the  present  work. 

77 


78  THE  RATE  OF  INTEREST  [Chap.  V 

Yet  the  fact  that  both  sets  of  goods  are  measured  in  money 
introduces  a  monetary  factor  into  the  problem  of  interest. 
Interest,  being  a  premium  in  the  exchange  between  the 
money  values  of  this  year's  and  next  year's  goods,  is  there- 
fore not  wholly  an  affair  of  goods,  but  is  partly  one  of  money. 
The  relation  of  the  rate  of  interest  to  goods  will  form  the 
subject  of  subsequent  chapters.  The  present  chapter 
is  devoted  to  a  study  of  the  relation  which  subsists  between 
the  rate  of  interest  and  the  monetary  standard  in  terms  of 
which  it  is  expressed. 

The  monetary  standard  affects  the  rate  of  interest  in 
so  far  as  there  is  a  change  in  the  value  of  that  standard 
in  reference  to  other  standards.  Could  it  always  be  as- 
sumed that  the  monetary  standard  was  invariable  in  value 
with  reference  to  all  goods,  the  rate  of  interest  reckoned 
in  money  would  be  the  same  as  though  it  were  reckoned 
in  terms  of  the  goods  themselves.  But  if  money  and  goods 
are  to  change  with  reference  to  each  other  —  in  other  words, 
if  the  money  standard  "appreciates"  or  "depreciates" 
—  the  number  expressing  the  rate  of  interest  will  be  affected. 

§2 

The  influence  of  monetary  appreciation  or  depreciation 
on  the  rate  of  interest  will  be  different  according  to  whether 
or  not  that  appreciation  or  depreciation  is  foreseen.  If  it 
is  not  foreseen,  the  appreciation  of  money  necessarily  in- 
jures the  debtor,  because,  the  purchasing  power  of  money 
being  increased,  the  principal  of  his  debt,  when  due,  repre- 
sents a  larger  quantum  of  goods  than  was  anticipated  when 
the  debt  was  contracted.  But  if  the  appreciation  is  fore- 
seen, any  increased  burden  in  the  "principal"  may  be  offset 
by  a  reduction  in  the  rate  of  interest.  This  fact,  strangely 
enough,  has  seldom  been  recognized.  The  assumption 
has  been  tacitly  made  that  contracting  parties  are  power- 
less to  forestall  gains  or  losses  due  to  an  upward  or  down- 
ward movement  of  the  monetary  standard.    Yet  no  reason 


Sec.  2]  APPRECIATION  AND  INTEREST  79 

has  been  given  to  show  that  it  is  any  more  difficult  to  make 
allowance  for  a  change  in  the  unit  of  value  than  for  a  change 
in  any  other  unit.  If  the  unit  of  length  were  changed,  and 
its  change  were  foreknown,  it  is  clear  that  contracts  would 
be  modified  accordingly.  Suppose,  for  instance,  that  a 
yard  were  defined  (as  possibly  it  once  was)  as  the  length 
of  the  king's  girdle,  and  suppose  the  king  to  be  a  child. 
Everybody  would  then  know  that  the  "yard"  would 
probably  increase  with  the  king's  age,  and  a  merchant 
who  should  agree  to  deliver  one  thousand  "yards"  ten 
years  hence  would  make  his  terms  correspond  to  his  ex- 
pectations. It  would  be  strange  if,  in  some  similar  way, 
an  escape  could  not  be  found  from  the  effects  of  changes 
in  the  monetary  yardstick,  provided  these  changes  were 
known  in  advance.  To  offset  a  foreseen  appreciation,  it 
would  only  be  necessary  that  the  rate  of  interest  be  cor- 
respondingly lower,  and  to  offset  a  foreseen  depreciation, 
that  it  be  correspondingly  higher.^ 

If  a  debt  is  contracted  optionally  in  either  of  two  stand- 
ards and  one  of  them  is  expected  to  change  with  reference 
to  the  other,  the  rate  of  interest  will  by  no  means  be  the 
same  in  both.  A  few  years  ago,  during  the  uncertainty 
as  to  the  adoption  or  rejection  of  "free  silver,"  a  syndicate 
offered  the  United  States  government  the  alternative  of 
some  $65,000,000  of  bonds  on  a  3  per  cent,  basis  in  gold, 
or  on  a  3f  per  cent,  basis  in  "coin."  Every  one  knew  that 
the  additional  f  per  cent,  in  the  latter  alternative  was  due 
to  the  mere  possibility  that  "coin"  might  not  continue  at 
full  gold  value,  but  sink  to  the  level  of  silver.  If  the 
alternative  had  been  between  repayment  in  gold  and  a  — 
not  merely  possible  but  actual  —  repayment  in  silver, 
the  additional  interest  would  obviously  have  exceeded 
f  per  cent. 

'  For  the  history  of  the  theory  of  appreciation  and  interest,  see 
Appendix  to  Chap.  V,  §  1. 


80  THE  RATE  OF  INTEREST  [Chap.  V 

§  3 

The  relation  between  the  rate  of  interest  and  the  rate 
of  a  foreseen  appreciation  or  depreciation  of  money  may 
be  readily  illustrated.  In  order  to  illustrate  the  theory, 
we  may  imagine  two  specified  standards  of  value  diverging 
from  each  other,  in  either  of  which  loan  contracts  may  be 
expressed.  Let  the  two  standards  be  gold  and  wheat, 
and  let  a  bushel  of  wheat  be  first  worth  $1.  If  the  two 
standards  did  not  diverge,  that  is,  if  the  price  of  wheat 
in  terms  of  gold  held  good  till  next  year,  it  is  clear  that 
the  rate  of  interest  in  a  gold  contract  and  a  wheat  contract 
would  be  the  same;  if  it  were  4  per  cent,  in  gold,  it  would 
be  4  per  cent,  in  wheat  also.  This  may  be  expressed  as 
follows :  — 

If  to-day  100  dollars  is  the  equivalent  of  100  bu.  @  $1  per  bu., 
then  next  year  104  dollars  is  the  equivalent  of  104  bu.  @  $1  per  bu. 

But  let  us  suppose  that  the  price  of  wheat  rises  from  $1 
to  $1.01.     We  then  readily  see  that :  — 

Whereas  to-day  100  dollars  is  the  equivalent  of  100  bu.  @  $1  per 
bu.,  next  year  104  x  1.01  dollars  is  the  equivalent  of  104  bu.  @  $1.01 
per  bu. 

If  we  calculate  out  the  104  x  $1.01,  we  shall  obtain  $105.04 
as  the  sum  which  next  year  should  be  repaid  in  gold  to  be 
equivalent  to  104  bu.  payable  in  wheat.  In  other  words,  if 
4  per  cent,  is  the  interest  in  the  wheat  standard,  its  equiva- 
lent is  5yoo  per  cent,  in  the  gold  standard;  or,  again,  if 
the  rate  of  interest  in  wheat  is  4  per  cent.,  an  appreciation 
of  wheat  of  1  per  cent,  is  exactly  offset  by  a  rise  of  1  ifg  P^^ 
cent,  in  the  rate  of  interest  in  gold.  It  is  thus  a  matter 
of  indifference  whether,  under  our  supposed  circumstances, 
a  man  who  borrows  $1000  expresses  his  contract  in  gold 
and  agrees  to  pay  5  y^g^  per  cent,  interest  or  translates  the 
same  contract  into  terms  of  wheat,  borrowing  the  value  of 


Sec.  4]  APPRECIATION  AND  INTEREST  81 

1000  bushels  and  agreeing  to  pay  4  per  cent,  interest.  By 
the  first  form  of  contract  he  pays  back  $1000  of  gold  prin- 
cipal and  $50.40  of  gold  interest ;  by  the  second,  he  pays 
back  the  value  of  1000  bu.  as  principal  and  of  40  bu.  as 
interest.  At  the  end  of  a  year  his  debt  by  the  one 
reckoning  is  $1050.40,  by  the  other,  1040  bu.,  and  these 
are  equivalent. 

It  is  to  be  noted  that  we  have  been  regarding  gold  or 
wheat  as  standards  of  value  and  not  as  media  of  exchange. 
In  either  contract  the  actual  liquidation  need  not  be  made 
either  in  actual  gold  or  wheat.  The  speculator  who  sells 
wheat  "short"  comes  very  close  to  using  wheat  as  a 
standard,  but  not  as  a  medium. 

The  relative  change  in  the  two  standards  may  be  spoken 
of  either  as  an  appreciation  of  wheat  relatively  to  gold, 
or  as  a  depreciation  of  gold  relatively  to  wheat.  We  are 
not  compelled  to  inquire  which  is  the  "absolute"  change. 
If  we  use  the  first  of  these  two  modes  of  expression,  we  may 
say  that  since  one  bushel  changes  in  value  from  $1  to  $1.01, 
wheat  has  appreciated  1  per  cent. ;  if  we  use  the  second  mode 
of  expression,  we  may  say  a  gold  dollar  has  fallen  in  its 
wheat  value  from  one  bushel  to  \^^  of  a  bushel,  and  has 
therefore  depreciated  by  -^1^  or  .OOy^j  per  cent.^ 


§  4 

In  oiu-  numerical  example,  the  appreciation  (1  per  cent.) 
of  one  standard  relatively  to  the  other,  and  likewise  the  de- 
preciation (.99  j^  J-  per  cent.)  of  the  latter  standard  relatively 
to  the  former,  are  not  quite  so  great  as  the  difference 
(lyo  0  psr  cent.)  in  the  rate  of  interest.  This  slight  disparity 
must  always  exist  so  long  as  the  rate  of  interest  is  reckoned 
annually  or  discontinuously.  But  the  shorter  the  period  of 
"compounding,"  the  less  the  disparity;  that  is,  the  more 

^  For  the  general  formula  connecting  the  rates  of  interest  in  any 
two  diverging  standards,  see  Appendix  to  Chap.  V,  §  2. 

G 


82  THE  RATE  OF  INTEREST  [Chap.  V 

nearly  equal  are  the  two  magnitudes:  (1)  the  rate  of 
divergence  between  the  two  standards,  whether  measured 
as  appreciation  or  depreciation,  and  (2)  the  difference 
between  the  rates  of  interest  in  the  two  standards.  When 
the  rates  are  "reckoned  continuously,"  the  disparity  dis- 
appears altogether/ 

§5 

Having  established  the  truth  and  generality  ^  of  the 
principle  connecting  the  rates  of  interest  in  two  standards 
and  the  appreciation  of  one  of  them  relatively  to  the  other, 
we  next  inquire  what  limits,  if  any,  are  imposed  on  the 
three  magnitudes;  namely,  the  two  rates  of  interest  in 
the  respective  standards  and  the  rate  of  relative  apprecia- 
tion between  the  standards.  From  what  has  been  said 
it  might  seem  that,  when  the  appreciation  is  sufficiently 
rapid,  the  rate  of  interest  in  the  upward-moving  standard, 
in  order  to  equalize  the  burden,  would  have  to  be  zero  or 
even  negative.  For  instance,  if  the  rate  of  interest  in  gold 
is  4  per  cent.,  and  if  wheat  appreciates  relatively  to  gold 
at  4  per  cent,  also,  the  rate  of  interest  in  wheat,  if  perfectly 
adjusted,  would  have  to  sink  to  zero !  But  we  know  that 
zero  or  negative  interest  is  practically  impossible.  Wheat 
would  be  hoarded,  and  this  action  would  effectually  pre- 
vent the  rate  of  interest  in  terms  of  wheat  from  passing 
below  the  zero  mark.  But  this  very  limitation  on  the 
possible  rate  of  interest  carries  with  it  a  limitation  on  the 

*  For  the  mathematical  demonstration  of  this  proposition,  see 
Appendix  to  Chap.  V,  §  3.  For  the  significance  of  "continuous" 
reckoning,  see  The  Nature  of  Capital  and  Income,  Chap.  XII;  also 
Chap.  XIII  and  Appendix.  We  have  here  an  example  of  the  fact 
there  observed  that,  considered  mathematically,  the  analytical  rela- 
tions connected  with  the  rate  of  interest  are  simplest  when  that  rate 
is  reckoned  continuously.  Since,  however,  the  rate  of  interest  reck- 
oned continuously  is  so  rarely  used  in  practice,  we  shall  adhere,  in 
the  remainder  of  our  discussion,  to  the  system  of  annual  reckoning. 

*  For  mathematical  proofs,  numerical  illustrations,  and  formulae 
see  Appendix  to  Chap.  V,  §§  4  to  9  inclusive. 


Sec.  5]  APPRECIATION  AND  INTEREST  83 

possible  rate  of  appreciation.  If  interest  on  money,  for 
instance,  were  4  per  cent.,  it  would  be  impossible  for  wheat 
to  have  a  foreknown  appreciation  of  10  per  cent,  per  an- 
num relatively  to  money;  for  it  would  immediately  be 
bought  and  held  for  the  rise.  It  would  therefore  rise  at 
once  to  the  discounted  value  of  its  future  expected  value, 
and  its  succeeding  rise  could  not  exceed  the  rate  of  inter- 
est,^ In  other  words,  if  interest  is  4  per  cent.,  it  is  impos- 
sible that  wheat  should  be  worth  $1  to-day  and  $1.10  next 
year  foreknown  to-day.  For,  under  these  circumstances, 
holding  for  a  rise  would  give  a  sure  return  of  10  per  cent. 
The  lowest  price  of  present  wheat  possible  would  be  the 
$1.10  discounted  at  4  per  cent.,  or  about  $1.06.  At  this 
figure  the  rate  of  interest  in  gold  is  4  per  cent.,  but  in 
wheat  it  is  zero  per  cent.     We  should  have :  — 

To-day  %  106  equivalent  to  100  bu.  @  $  1.06  per  bushel. 
Next  year  $  110  equivalent  to  100  bu.  @  $  1.10  per  bushel. 

and  the  two  alternative  forms  of  contract  would  be:  for 
$106  this  year  $110  are  returned  next  year,  or  (about)  4 
per  cent.,  and  for  100  bu.  this  year  100  bu.  are  returned 
next  year,  or  zero  per  cent.  Every  case  of  holding  wheat 
or  land  or  other  wealth  for  a  rise  may  be,  in  fact,  regarded 
as  a  case  of  zero  interest  in  terms  of  these  articles  as 
standards  of  value. 

The  same  principle  which  prevents  the  rate  of  interest 
in  wheat  or  land  from  being  negative  also  prevents  a 
negative  interest  in  money.  A  lender,  rather  than  ex- 
change $101  to-day  for  $100  next  year,  would  hoard  his 
$101.  It  is  important  to  emphasize  the  fact  that  the  limits 
imposed  on  the  rates  of  interest  and  appreciation  come 
from  the  possibility  of  hoarding  money  without  loss.  If 
money  were  a  perishable  commodity,  like  fruit,  the  limit 
would  be  pushed  into  the  region  of  negative  quantities. 

'  See  The  Nature  of  Capital  and  Income,  on  the  rate  of  rise  of  "  dis- 
count curves,"  Chap.  XIII. 


84  THE  RATE  OF  INTEREST  [Chap.  V 

One  can  imagine  a  loan  based  on  strawberries  or  peaches, 
contracted  in  summer  and  payable  in  winter,  with  negative 
interest.^  Or,  again,  we  may  define  a  "dollar"  as  consist- 
ing of  a  constantly  increasing  number  of  grains  of  gold, 
the  weight  of  which  is  to  double  yearly.  Such  "dollars" 
cannot  he  hoarded  without  necessarily  becoming  fewer  with 
time,  and  if  interest  in  the  old  fixed-weight  dollars  is  5  per 
cent.,  it  will  be  minus  47 1  per  cent,  in  the  new  dollars  of 
increasing  weight;  for  he  who  borrows  $100  (2580  grains) 
to-day  will  need  to  pay  back  only  $52.50  (2709  grains) 
one  year  hence. 

§6 

The  relation  existing  between  interest  and  apprecia- 
tion implies,  then,  that  the  "rate  of  interest"  is  always 
relative  to  the  standard  in  which  it  is  expressed.  The 
fact  that  interest  in  money  is  high,  say  15  per  cent.,  may 
merely  indicate  that  general  prices  are  expected  to  rise 
at  the  rate  of  10  per  cent.,  and  that  the  rate  of  interest  in 
terms  of  goods  is  not  high,  but  only  4^  per  cent. 

We  thus  need  to  distinguish  between  interest  in  terms 
of  money  and  interest  in  terms  of  goods.  The  first  thought 
suggested  by  this  fact  is  that  the  rate  of  interest  in  money 
is  "nominal,"  and  that  in  goods  "real."  But  this  distinc- 
tion is  not  sufficient,  for  no  two  forms  of  goods  maintain, 
or  are  expected  to  maintain,  a  constant  price  ratio  tow- 
ard each  other.  There  are  therefore  just  as  many  rates 
of  interest  in  goods  as  there  are  forms  of  goods  diverging  in 
valy£. 

Is  there,  then,  no  absolute  standard  of  value,  as  utility, 
in  terms  of  which  "real"  interest  should  be  expressed? 
To  this  we  reply  that  any  absolute  standard  is  absolute 
only  for  a  particular  individual.^     The  fact  that  a  dollar 

1  Cf.  Bohm-Bawerk,  The  Positive  Theory  of  Capital,  pp.  252,  297; 
Landry,  L' Intent  du  Capital,  p.  49. 

^  Marshall,  Principles  of  Economics,  Vol.  I,  3d  ed.  New  York 
(Macmillan) ,  1895,  p.  198,  and  Royal  Commission  on  Depression  of 


Sec.  6]  APPRECIATION  AND  INTEREST  85 

is  a  smaller  unit  to  a  millionaire  than  to  a  poor  laborer 
has  as  its  consequence  that,  as  the  millionaire  grows  poorer 
his  dollar  grows  larger,  while  as  the  laborer  grows  richer 
his  dollar  grows  smaller.  On  account  of  such  changes  in 
personal  fortunes,  the  dollar  will  be  constantly  appreciat- 
ing and  depreciating  in  different  degrees  among  different 
men  and  classes.  But  if  the  dollar  appreciates  in  terms 
of  absolute  utility  in  the  eyes  of  one  man,  and  depreciates 
in  a  corresponding  standard  of  utility  in  the  eyes  of  another, 
the  rates  of  interest  in  the  men's  "absolute"  standards 
must  be  different  in  the  two  cases;  for  the  rates  of  in- 
terest to  both  persons  in  terms  of  objective  imits,  such  as 
money,  must  hy  the  operations  of  the  market  he  the  same. 
If,  in  the  gold  standard,  $100  to-day  is  equivalent  to  S104 
due  one  year  hence,  both  for  him  who  is  gi-owing  richer 
and  for  him  who  is  growing  poorer,  the  rates  in  terms  of  ab- 
solute utility  will  be  different  for  the  two  men.  Thus,  sup- 
pose that  the  dollar  to-day  is  worth  to  each  man  one  unit  of 
utility,  but  that  one  year  hence,  to  the  man  who  is  gi'owing 
richer,  the  dollar  will  be  worth  slightly  less  — let  us  say, 
^Q%  of  one  unit  of  utility.  Consequently,  when  he  considers 
$100  to-day  as  equivalent  to  $104  due  next  year,  he  is 
virtually  contrasting  in  his  mind  100  units  of  utility  to-day 
with  104  X  .99,  or  about  103  units  of  utility  next  year.  His 
rate  of  interest,  therefore,  in  terms  of  absolute  utility,  is 
3  per  cent.  Similar  calculations  for  the  man  whose  for- 
tunes were  declining,  and  to  whom  the  marginal  utility  of 
the  dollar  was  increasing  1  per  cent,  per  annum,  would 
show  that  whereas  $100  to-day  is  equivalent  in  his  esti- 
mation to  $104  next  year,  100  units  of  present  utility  are 
equivalent  to  about  105  units  of  next  year's  utility.  To 
him,  therefore,  the  rate  of  interest  in  the  absolute  standard 
would  be  5  per  cent. 

Trade,  1886,  p.  423;  the  writer's  "Mathematical  Investigations  in 
the  Theory  of  Value  and  Prices,"  Transactions  of  the  Connecticut 
Academy,  New  Haven,  1892,  pp.  11-23,  86-89;  A.  C.  Pigou,  "Some 
Remarks  on  Utility,"  Economic  Journal,  March,  1903,  p.  60. 


86  THE  RATE  OF  INTEREST  [Chap.  V 

From  this  explanation  it  is  very  evident  that  if  we  seek 
to  postulate  an  absolute  standard  of  value  in  which  the 
rates  of  interest  are  to  be  reckoned,  we  cannot  fix  one 
which  will  be  uniform  for  all  the  individuals  in  the  market. 
Supply  and  demand  operate  only  to  make  objective  rates 
equal.  Hereafter  we  shall  confine  ourselves  to  a  study  of 
objective  interest;  and  since  the  objective  standard  usually 
employed  is  money,  the  rate  of  interest,  unless  otherwise 
specified,  will  be  taken  in  this  book  to  mean  the  rate  of 
interest  in  terms  of  the  money  standard. 

As  was  observed  at  the  beginning  of  this  chapter,  it 
makes  a  great  difference  whether  the  relative  divergence  of 
the  different  standards  is  or  is  not  known  in  advance. 
In  actual  fact  it  usually  happens  that  future  appreciation 
or  depreciation  is  neither  entirely  foreseen  nor  entirely 
unforeseen.  An  intermediate  condition  is  usually  main- 
tained. When  prices  are  rising,  the  rate  of  interest  is 
usually  high,  but  not  as  high  as  it  should  be  to  compensate 
for  the  rise ;  and  when  prices  are  falling,  the  rate  of  interest 
is  usually  low,  but  not  as  low  as  it  should  be  to  compensate 
for  the  fall.  The  facts  as  they  are  actually  found  in  the 
market  will  be  given  in  Chapter  XIV. 


CHAPTER  VI 

TIME-PREFERENCE 
§1 

In  the  last  chapter  we  saw  that  the  number  expressing 
the  rate  of  interest  depends  on  the  standard  of  value  in 
which  present  and  future  goods  are  expressed.  We  saw 
how  the  rate  of  interest  in  one  standard  is  to  be  derived 
from  the  rate  of  interest  in  any  other  standard. 

It  is  clear  that  this  translation  of  the  rate  of  interest 
from  one  standard  to  another  does  not  constitute  a  com- 
plete determination  of  the  rate  of  interest  in  any  standard 
whatever ;  for  it  assumes  that  the  rate  in  some  one  standard 
is  already  known,  and  merely  enables  us  on  the  basis  of 
this  known  rate  to  calculate  the  rates  in  other  standards. 
The  case  is  similar  to  the  conversion  of  temperature  from 
the  Fahrenheit  system  into  the  Centigrade  or  the  Reaumur, 
which  clearly  does  not  determine  temperature  itself;  or,  to 
the  conversion  of  the  price  of  cotton  in  dollars  into  its  price 
in  shiUings  or  francs,  which  does  not  determine  the  price  of 
cotton  itself.  Tlie  relation  which  has  been  shown  between 
appreciation  (or  depreciation)  and  interest  therefore  solves 
merely  the  problem  of  translating  the  rate  of  interest  from 
one  standard  into  another ;  but  the  problem  of  deter7nining 
the  rate  of  interest  is  still  left  untouched.  This  problem 
—  the  problem  of  determining  the  rate  of  interest  —  now 
demands  attention. 

In  our  theory  we  shall  find  a  place  for  each  of  the  partial 
truths  which  we  have  found  in  the  foregoing  review  of  the 
productivity,  cost,  and  agio  theories.  Our  presentation 
may,  in  fact,  be  classified  as  a  form  of  the  agio  theory,  differ- 
ing from  Bohm-Bawerk's  version  chiefly  by  the  omission  of 

87 


88  THE  RATE  OF  INTEREST  [Chap.  VI 

the  "technical  advantage  of  present  over  future  goods," 
and  from  agio  theories  in  general  by  the  explicit  introduc- 
tion of  the  income-concept.  The  income-concept  plays  the 
central  role. 

The  theory  of  interest  bears  a  close  resemblance  to  the 
theory  of  prices,  of  which,  in  fact,  it  might  be  regarded  as  a 
part;  for,  as  was  shown  in  The  Nature  of  Capital  and 
Income,  Chap.  XII,  the  rate  of  interest  expresses  a  price 
in  the  exchange  between  present  and  future  goods.  Just 
as  in  the  ordinary  theory  of  prices  the  ratio  of  exchange 
of  any  two  articles  is  based  on  a  psychological  or  sub- 
jective element,  —  their  comparative  marginal  utility,  — 
so  in  the  theory  of  interest  the  rate  of  interest,  or  the  pre- 
mium in  the  exchange  between  present  and  future  goods, 
is  based  on  a  subjective  prototype;  namely,  the  preference 
for  present  over  future  goods. 

This  "time-preference"  is  the  central  fact  in  the  theory 
of  interest.^  It  is  what  Rae  calls  the  "effective  desire  for 
accumulation,"  and  very  nearly  what  Bohm-Bawerk  calls 
the  "perspective  undervaluation  of  the  future."  ^  It  is  the 
(percentage)  excess  of  the  present  desirability  ^  of  present 
goods  over  the  present  desirability  of  an  equal  amount  of 
future  goods. 

1  Cf.  Bullock,  Introduction  to  the  Study  of  Economics  (Silver,  Bur- 
dett  &  Company),  1900,  p.  390;  Fetter,  Economics,  New  York  (Century 
Co.),  1904,  p.  135. 

^  At  least,  as  applied  to  objective  goods.  Bohm-Bawerk  applies 
it  to  subjective  pleasures,  which  he  translates  into  objective  goods 
at  a  ratio  depending  on  the  "relative  provision  for  present  and  future 
needs."  As  we  have  seen  in  §  6  of  the  preceding  chapter,  it  is  possible 
to  translate  the  rate  of  interest  (and,  it  might  have  been  added,  the 
rate  of  preference)  from  an  objective  to  a  subjective  standard,  or  vice 
versa,  provided  we  know  the  rate  at  which  the  two  standards  are 
diverging.  We  prefer  to  base  our  reasoning  in  this  book  on  rates  of 
preference  and  rates  of  interest  expressed  in  terms  of  an  objective, 
monetary  standard.  As  we  have  seen,  the  rate  of  preference  ex- 
pressed in  terms  of  subjective  standards  will  be  different  for  different 
individuals . 

■■'  Or  "ophelimity,"  or  "utility."  See  The  Nature  of  Capital  and 
Income,  Chap.  III. 


Sec.  2]  TIME-PREFERENCE  89 

§  2 

But  what  are  these  "goods"  which  are  thus  contrasted? 
At  first  sight  it  might  seem  that  the  "goods"  compared 
may  be  indiscriminately  wealth,  property,  or  services.^  It  is 
true  that  present  machines  are  preferred  to  future  machines ; 
present  houses  to  futm-e  houses;  land  possessed  to-day 
to  land  available  next  year;  present  food  or  clothing  to 
future  food  or  clothing;  present  stocks  or  bonds  to  future 
stocks  or  bonds;  present  music  to  future  music,  and  so  on. 
But  a  slight  examination  will  show  that  some  of  these 
cases  of  preference  are  reducible  to  others.  Wlien  present 
capital  (whether  capital-wealth  or  capital-property)  is  pre- 
ferred to  future  capital,  this  preference  is  really  a  prefer- 
ence for  the  income  of  the  first  capital  as  compared  with 
the  income  of  the  second.  The  reason  we  would  choose  a 
present  fruit  tree  rather  than  a  similar  tree  available  in 
ten  years  is  that  the  fruit  production  of  the  first  wiU  occur 
earlier  than  that  of  the  second.  The  reason  one  prefers 
immediate  tenancy  of  a  house  to  the  right  to  occupy  it  in 
six  months  is  that  the  uses  of  the  house  begin  six  months 
earlier  in  one  case  than  in  the  other.  In  short,  capital- 
wealth  available  early  is  preferred  to  capital-wealth  of 
like  kind  available  at  a  more  remote  time,  because  the 
income  of  the  former  is  available  earlier  than  the  income 
of  the  latter.  For  the  same  reason,  early  capital-property 
is  preferred  to  late  capital-property  of  the  same  description. 
For  property  is  merely  a  claim  to  future  income ;  and  the 
earlier  the  property  is  acquired,  the  earlier  will  the  in- 
come accrue,  of  the  right  to  which  the  property  consists. 

Thus,  all  time-preference  resolves  itself  into  the  prefer- 
ence for  early  income  over  late  income.  Moreover,  the 
preference  for  present  income  over  future  income  resolves 
itself  into  the  preference  for  present  final  income  over  future 
final  income.    The  income  from  an  article  of  capital  which 

*  For  definitions  of  these  terms,  see  Glossary. 


90  THE  RATE  OF  INTEREST  [Chap.  VI 

consists  merely  of  an  "interaction"  ^  or  "preparatory  ser- 
vice"^ is  desired  for  the  sake  of  the  final  income  to  which 
that  interaction  paves  the  way.  We  prefer  present  bread 
baking  to  future  bread  baking  because  the  enjoyment  of  the 
resulting  bread  is  available  earlier  in  the  one  case  than  in 
the  other.  Present  weaving  is  preferred  to  future  weaving, 
because  the  earlier  the  weaving  takes  place  the  sooner  will 
the  cloth  be  manufactured,  and  the  sooner  will  the  clothing 
made  from  it  be  worn  by  the  consumer. 

When,  as  is  usually  the  case,  exchange  intervenes  be- 
tween the  weaving  and  the  use  of  the  clothes,  the  goal  in 
the  process  is  somewhat  obscured  by  the  fact  that  the 
manufacturer  feels  his  preference  for  present  weaving  over 
future  weaving,  not  because  the  clothes  will  be  more  early 
available,  but  because  he  will  be  enabled  to  sell  the  cloth 
earlier.  To  him,  early  sales  are  more  advantageous  than 
deferred  sales,  because  the  earlier  the  money  is  received  the 
earlier  can  he  spend  it  for  his  own  personal  uses,  —  the  shel- 
ter and  the  comforts  of  various  kinds  constituting  his  real 
income.  It  is  not  he,  but  his  customers,  those  who  buy 
the  cloth  he  manufactures,  that  base  their  preference  for 
present  cloth  over  future  cloth  on  the  earlier  availability  of 
the  clothes  which  can  be  made  from  it.  But  in  both  cases 
the  mind's  eye  is  fixed  on  some  ultimate  enjoyable  income 
to  which  the  interaction  in  question  is  a  mere  preparatory 
step.  We  thus  see  that  all  preference  for  present  over 
future  goods  resolves  itself,  in  the  last  analysis,  into  a 
preference  for  early  enjoyable  income  over  late  enjoyable 
income.  This  simple  proposition  would  have  received 
attention  before  had  there  been  at  hand  a  clear-cut  con- 
cept of  income. 

§  3 

In   The  Nature  of  Capital  and  Income  ^  it  was  shown 
that  income  ultimately  consists  of  the  stream  of  conscious- 

*  See  Glossary. 

*  See  The  Nature  of  Capital  and  Income,  Chap.  IX. 
5  Chap.  X. 


Sec.  3]  TIME-PREFERENCE  91 

ness.  Or,  if  we  prefer  to  stop  just  short  of  this  subjective 
income,  we  may  say  that  income  consists  of  the  objective 
services  which  impinge  upon  our  persons  and  are  on  the 
point  of  producing  the  subjective  effects  on  consciousness. 
In  short,  the  income-stream  consists  of  nourishment,  cloth- 
ing, shelter,  amusements,  the  gratification  of  vanity,  and 
other  miscellaneous  items.  It  is  this  income-stream  upon 
which  attention  now  centers.  Henceforth,  instead  of 
speaking  vaguely  and  loosely  of  the  preference  for  present 
"goods"  over  future  "goods,"  we  shall  speak  of  the  prefer- 
ence for  present  enjoyable  income  over  future  enjoyable  in- 
come. "Present"  and  "future"  are,  of  course,  used  in  a 
comparative  sense  only;  in  a  more  accurate  statement  we 
should  substitute  "early"  and  "deferred." 

It  should  be  noted  that  the  preference  for  present  over 
future  goods,  when  thus  reduced  to  its  lowest  terms,  rids 
the  values  of  the  contrasted  present  and  future  goods  of 
the  interest  element.  When  any  other  goods  than  enjoy- 
able income  are  considered,  their  values  already  imply  a 
rate  of  interest.  When  we  say  that  interest  is  the  premium 
on  the  value  of  a  present  house  over  that  of  a  future  house, 
we  are  apt  to  forget  that  the  value  of  each  house  is  itself 
based  on  a  rate  of  interest.  We  have  seen  *  that  the  price 
of  a  house  is  the  discounted  value  of  its  future  income.  In 
the  process  of  discounting  there  lurks  a  rate  of  interest. 
The  value  of  houses  will  rise  or  fall  as  the  rate  of  interest 
falls  or  rises.  Hence,  when  we  compare  the  values  of  present 
and  future  houses,  both  terms  of  the  comparison  involve 
the  rate  of  interest.  If,  therefore,  we  undertake  to  make 
the  rate  of  interest  depend  on  the  relative  preference  for 
present  over  future  houses,  we  are  making  it  depend  on 
two  elements,  in  each  of  which  it  already  enters.  The  same 
is  true  of  all  capital,  and  also  of  those  items  of  income 
which  we  have  called  interactions;  for  the  value  of  an 
interaction  is  the  discounted  value  of  the  ultimate  income 

•  See  supra,  Chap.  II,  and  The  Nature  of  Capital  and  Income, 
Chap.  XIII. 


92  THE  RATE  OF  INTEREST  [Chap.  VI 

to  which  that  interaction  leads.  We  could  not  rest  satisfied 
in  the  statement  that  interest  is  the  premium  on  the 
value  of  present  tree-planting  over  that  of  future  tree- 
planting;  for  the  value  of  each  tree-planting  itself  depends 
on  the  rate  at  which  the  future  income  from  the  tree  is 
discounted.  But  when  present  ultimate  income  is  com- 
pared with  future  ultimate  income,  the  case  is  different, 
for  the  value  of  ultimate  income  involves  no  interest  what- 
ever. We  see,  therefore,  that  the  reduction  of  the  problem 
of  interest  to  a  comparative  value  of  present  and  future 
enjoyable  income  avoids  the  difficulty  of  making  interest 
depend  on  magnitudes  which  themselves  depend  directly 
on  interest. 

§4 

Having  seen  that  time-preference  is  really  a  preference 
for  early  enjoyable  income  compared  with  remote  enjoy- 
able income,  we  next  note  that  this  preference  depends 
on  the  entire  future  income-stream,  that  is,  the  amount  of 
income  and  the  manner  in  which  it  is  distributed  in  time. 
It  depends  on  the  relative  abundance  of  the  early  and 
remote  incomes  —  or  what  we  may  call  the  time-shape  of 
the  income-stream.  If  future  income  is  particularly  abun- 
dant, its  possessor  would  evidently  be  willing  to  sacrifice 
a  large  amount  of  it  for  the  sake  of  a  relatively  small 
amount  of  present  income.^  Thus,  in  winter,  the  possessor 
of  a  strawberry  patch  might  be  willing  to  sell  two  boxes  of 
strawberries,  due  in  six  months,  for  one  available  to-day, 
while  in  strawberry  season  he  might,  on  the  contrary,  be 

'  It  is  noteworthy  that,  though  lacking  any  definite  theory  of 
income,  those  writers  who  have  made  the  most  successful  analysis 
of  the  rate  of  interest  have,  in  substance,  made  it  depend,  to  some 
extent,  at  least,  on  income.  Thus  Bohm-Bawerk,  as  has  been  observed, 
gives  as  one  of  the  "three  circumstances"  aflfecting  the  "preference 
for  present  goods"  the  "relative  provision  for  present  and  future"; 
and  Landry  virtually  states  the  same  relation,  on  p.  55  of  L'InUret 
du  Capital. 


Sec.  4]  TIME-PREFERENCE  93 

willing  to  give  up  two  boxes  of  his  then  abundant  crop  for 
the  right  to  one  box  in  the  succeeding  winter. 

It  is,  therefore,  not  necessary  here   to   distinguish,   as  ' 

Bohm-Bawerk  does,  between  the  principles  which  lead  to  the 
existence  of  interest  and  those  which  regulate  the  rate  of 
interest;  for  to  determine  the  rate  of  interest  will  include 
the  determination  of  whether  the  rate  must  necessarily  i 

always  be  greater  than  zero.  As  a  matter  of  fact,  the  rate 
may  theoretically  be  negative,  as  in  the  case  just  mentioned  j 

of  strawberries  in  strawberry  season,  or  in  the  case  cited  by  ^ 

Bohm-Bawerk  himself,  of  ice  in  wmter.  The  reason  such 
negative  interest  is  not  actually  encountered  in  the  market 
is  that  perishable  articles  such  as  ice  and  strawberries  are 
never  used  as  standards  of  value.  We  express  our  rates 
of  interest  in  money,  even  if  our  contracts  relate  to 
strawberries  or  ice.  But  money  possesses  durability,  and 
may  be  hoarded  without  loss.  Tliis  explains  why  the 
rate    of    interest    in    terms    of    money    can    never    be  1 

negative.^  j 

The  proposition  that  the  preference  of  any  individual  f 

for  present  over  future  income  depends  upon  his  pro- 
spective enjoyable  income  corresponds  to  the  proposition  in 
the  theory  of  prices,  that  the  marginal  utility  of  any  article 
depends  upon  the  quantity  of  that  article;  both  proposi- 
tions are  fmidamental  in  their  respective  spheres. 

Wlien  it  is  said  that  the  time-preference  of  an  individual 
depends  on  his  enjoyable  income,  it  is  meant  that  the  rate  j 

of  preference  for,  say,  $100  worth  of  this  year's  enjoyable  ' 

income  over  $100  worth  of  next  year's  enjoyable  income 
depends  upon  the  entire  character  of  the  individual's  in-  i 

come-stream. 

An  income-stream   is   made  up  of  a  large  number  of  1 

different  elements,  some  of  which  contribute  to  nourish- 
ment, others  to  shelter,  others  to  amusement,  etc.     In  a  ] 
complete  enumeration  of  these  elements,  we  should  need 
to  distinguish  the  use  of  each  different  kind  of  food,  the  j 

'■  See  Sujjra,  Chap.  V,  §  5. 


94  THE  RATE  OF  INTEREST  [Chap.  VI 

gratification  of  every  variety  of  human  want.  Each  of 
these  constitutes  a  particular  filament  of  the  income- 
stream,  extending  from  the  present  out  into  the  indefinite 
future  and  varying  at  different  points  of  time  in  respect 
to  size  and  probability  of  attainment.  A  man's  rate  of 
time-preference,  therefore,  depends  on  the  size  and  prob- 
ability at  various  moments  of  the  entire  collection  of 
income-elements.  For  the  graphic  representation,  how- 
ever, of  size  and  distribution  in  time,  it  is  simpler  to  lump 
together  these  innumerable  elements  of  income,  expressed 
in  terms  of  money.  We  may  say,  therefore,  that  an  indi- 
vidual's time-preference  depends  on  the  following  four 
elements :  — 

1.  On  the  size  of  the  income-stream. 

2.  On   its  distribution  in  time, — according   as  it  accrues 

evenly  or  unevenly,  and  if  imevenly,  according  to  the 
periods  at  which  it  is  expected  to  be  relatively  abun- 
dant and  the  periods  at  which  relatively  scarce. 

3.  On  the  composition  of  the  income-stream, — what  part 

consists  of  nourishment,  what  part  clothing,  what 
part  shelter,  etc. 

4.  On  the  probability  of  the  income-stream  and  its  con- 

stituent elements. 

We  shall  consider  these  in  order. 


Our  first  step,  then,  is  to  show  how  a  person's  time- 
preference  depends  on  the  size  of  his  income.  In  general, 
it  may  be  said  that  the  smaller  the  income  the  higher  is 
the  preference  for  present  over  future  income.  It  is  true 
that  a  small  income  implies  a  keen  appreciation  of  future 
wants  as  well  as  of  immediate  wants.  Poverty  bears  down 
heavily  on  all  parts  of  a  man's  life,  both  that  which  is  im- 


Sec.  6]  TIME-PREFERENCE  95 

mediate  and  that  which  is  remote.  But  it  enhances  the 
utihty  of  immediate  income  even  more  than  of  future  in- 
come. This  result  is  partly  rational,  because  of  the  im- 
portance, by  supplying  present  needs,  of  keeping  up  the 
continuity  of  hfe  and  the  ability  to  cope  with  the  future; 
and  partly  irrational,  because  the  pressure  of  present  needs 
blinds  one  to  the  needs  of  the  future.  As  to  the  rational 
side,  it  is  clear  that  present  income  is  absolutely  indispen- 
sable, not  only  for  the  present,  but  even  as  a  precondition 
to  the  attainment  of  future  income.  "A  man  must  live." 
Any  one  who  values  his  life  would  prefer  to  rob  the  future 
for  the  benefit  of  the  present,  so  far,  at  least,  as  to  keep  life 
going.  If  one  has  only  one  loaf  of  bread  he  would  not 
preserve  it  for  next  year;  for  if  he  did  he  would  starve  in 
the  meantime.  A  single  break  in  the  thread  of  life  suffices 
to  cut  off  all  the  future.  And  not  only  is  a  certain  mini- 
mum of  present  income  necessary  to  prevent  starvation, 
but  the  nearer  this  minimum  is  approached  the  more 
precious  does  present  income  appear,  relatively  to  future 
income. 

As  to  the  irrational  side,  the  effect  of  poverty  is  often 
to  relax  foresight  and  self-control  and  tempt  one  to  "trust 
to  luck"  for  the  future,  if  only  the  all-absorbing  clamor  of 
present  necessities  is  satisfied. 

We  see,  then,  that  a  low  income  tends  to  produce  a  high 
time-preference,  partly  from  lack  of  foresight  and  self-con- 
trol, and  partly  from  the  thought  that  provision  for  the 
present  is  necessary  both  for  itself  and  for  the  future 
as  well. 

§6 

We  come  next  to  the  influence  upon  time-preference  of 
the  distribution  of  income  in  time  —  the  time-shape  of  the 
income-stream.  The  concept  of  the  time-shape  of  one's 
income-stream  is  fundamental  in  the  following  chapters. 
Four  different  types  of  time-shape  may  be  distinguished : 


96 


THE  RATE  OF  INTEREST 


[Chap.  VI 


uniform  income,  as  represented  in  Figure   2;^  increasing 
income  (Fig.  3) ;  decreasing  income  (Fig.  4) ;  and  fluctuating 


Fig.  2. 


income  (Fig.  5).     The  effect  of  possessing  an  increasing  in- 
come is  to  make  the  preference  for  present    over   future 


Fig.  3. 


income  higher  than  otherwise,  for  it  means  that  present 
income  is  relatively  scarce  and  future  income  abundant. 


Fig.  4. 

A  man  who  is  now  enjoying  an  income  of  only  $1000  a 
year,  but  expects  in  ten  years  to  be  enjoying  one  of 
S 10 ,000  a  year,  will  prize  a  dollar  to-day  far  more  than  a 
doUar  due  ten  years   hence.     He    may,    in   fact,  borrow 

*  In  these  curves,  time  is  represented  horizontally  and  rate  of 
flow  of  income  vertically,  as  in  The  Nature  of  Capital  and  Income, 
Chap.  XIII. 


Sec.  6]  TIME-PREFERENCE  97 

money  to  eke  out  this  year's  income,  and  make  repayment 
by  sacrificing  from  the  more  abundant  income  ten  years 
later.  Reversely,  a  gradually  decreasing  income,  making, 
as  it  does,  present  income  relatively  abundant  and  future 
income  scarce,  tends  to  reduce  the  preference  for  present 
as  compared  with  future  income.  A  man  who  has  a  salary 
of  $10,000  at  present,  but  expects  to  retire  in  a  few  years 
on  half  pay,  will  not  have  a  very  high  preference 
for  present  income  over  future.  He  will  want  to  save 
from  his  present  abundance  to  provide  for  coming 
needs. 

The  extent  of  these  effects  will  of  course  vary  greatly  with 
different  individuals.     Corresponding  to  a  given  ascend- 


FiG.  5. 

ing  income,  one  individual  may  have  a  preference  of  10  per 
cent.,  and  another  only  4  per  cent.  ^Vhat  we  need  here 
to  emphasize  is  merely  that,  given  a  descending  instead 
of  an  ascending  income,  both  of  these  individuals  would 
experience  a  reduction  of  time-preference,  — the  first,  say, 
to  5  per  cent,  and  the  second,  say,  to  2  per  cent. 

If  we  consider  the  combined  effect  on  time-preference  of 
both  the  size  and  time-shape  of  income,  we  shall  observe 
that  those  with  small  incomes  are  much  more  sensitive  to 
time-shape  in  their  feeling  of  time-preference  than  are 
those  with  large  incomes.  For  a  poor  man,  a  very  slight 
stinting  of  the  present  suffices  to  enhance  enormously  his 
preference  for  present  over  future  income;  and  reversely, 
a  very  slight  increase  in  his  present  income  will  suffice  to 


98  THE  RATE  OF  INTEREST  [Chap.  VI 

enormously  lessen  that  preference.  A  rich  man,  on  the 
other  hand,  requires  a  relatively  large  variation  in  the 
comparative  amoimts  of  this  year's  and  next  year's  in- 
come to  suffer  any  material  change  of  time-preference. 

It  is  clear  that  the  dependence  of  time-preference  on 
time-shape  of  income  is  practically  identical  with  what 
Bohm-Bawerk  calls  the  "first  circumstance"  making  for 
the  superiority  of  present  over  future  goods :  ^ 

"The  first  great  cause  of  difference  in  value  between  present  and 
future  goods  consists  in  the  different  circumstances  of  want  and 
provision  in  present  and  future.  ...  If  a  person  is  badly  in  want 
of  certain  goods,  or  of  goods  in  general,  while  he  has  reason  to  hope 
that,  at  a  future  period,  he  will  be  better  off,  he  will  always  value 
a  given  quantity  of  immediately  available  goods  at  a  higher  figure 
than  the  same  quantity  of  future  goods." 


We  come  next  to  the  influence  of  the  composition  of  the 
income-stream  on  the  time-preference  of  its  possessor.  An 
income  worth  $5000  may,  for  one  individual,  comprise 
one  set  of  enjoyable  services,  and  for  another,  an  entirely 
different  set.  The  inhabitants  of  one  country  may  have 
relatively  more  house-shelter  and  less  food-element  in 
their  incomes  than  those  of  another.  These  differences 
will  have  an  influence  in  one  direction  or  the  other  upon 
the  time-preference.  Diminution  of  any  one  constituent  of 
income  would  have  an  effect  upon  the  time-preference 
similar  to  the  effect  of  diminution  of  income  in  general.  A 
decrease  of  the  food  element  would  be  felt  especially,  both 
because  this  element  usually  forms  a  considerable  part  of 
income  and  because  it  is  a  prime  necessity. 

Were  we  to  pursue  the  subject  in  detail,  we  should  need 
to  resolve  a  person's  income  into  the  elements  of  which  it 
is  composed,  — nourishment,  shelter,  clothing,  and  other 
gratifications.  As  we  have  seen,  the  income-stream  is  a 
complex  magnitude  consisting  of  a  large  number  of  sepa- 

'  The  Positive  Theory  of  Capital,  p.  249. 


Sec.  8]  TIME-PREFERENCE  99 

rate  filaments,  one  for  each  separate  constituent.  Any 
individual's  rate  of  preference  depends  on  this  complex 
magnitude  in  its  entirety.  Theoretically  a  change  in 
any  of  these  individual  partial  income-streams  will  in- 
fluence the  rate  of  preference.  A  bread  famine,  a  large 
wheat  crop,  the  outlook  for  the  fuel  supply,  electric  light 
service,  shoes,  or  diamonds,  all  should  be  taken  into  ac- 
count in  a  statement  designed  fully  to  cover  the  influence 
of  the  income-stream  upon  time-preference. 

It  is  not  necessary  to  formulate  the  concept  of  "com- 
position" of  an  income-stream  in  such  a  way  as  to  divorce 
it  from  the  concepts  of  size  and  time-shape ;  for  the  com- 
position of  an  income-stream  is  included  in  a  statement 
of  the  size  and  time-shape  of  each  filament  of  which  that 
income-stream  consists.  We  content  ourselves  by  con- 
sidering all  these  elements  of  income  lumped  together  in 
a  single  sum  of  money  value.  We  need  not  here  concern 
ourselves  with  the  principles  which  govern  the  valuation 
of  the  sum.  These  principles  constitute  the  theory  of 
prices,  not  of  interest;  and  these  prices,  as  we  have 
already  observed,  being  prices  of  final  or  enjoyable 
elements  of  income,  do  not,  like  the  prices  of  capital 
or  of  interactions,  embarrass  us  by  direct  dependence  on 
the  rate  of  interest  which  we  are  seeking  to  solve.  As- 
suming, then,  the  elements  of  which  incomes  are  composed 
to  be  adjusted  according  to  the  principles  which  regulate 
prices,  we  shall  hereafter  usually  treat  an  income-stream  as 
a  homogeneous  quantum  expressible  in  terms  of  gold  or 
some  other  monetary  standard.  Our  task  is  therefore  re- 
duced to  answering  the  question  :  Enjoyable  incomes  being 
expressed  in  terms  of  money,  what  determines  the  rate  of 
interest  in  terms  of  this  same  money? 

§  8 

We  come  finally  to  the  element  of  risk.  Income,  being 
future,  is  always  subject  to  some  uncertainty,  and  this  un- 


100  THE  RATE  OF  INTEREST  [Chap.  VI 

certainty  must  naturally  have  an  influence  on  the  rate  of 
time-preference  of  the  possessor.  We  have  seen  that  time- 
preference  is  the  preference  for  $1  certain  added  to  im- 
mediate income  over  $1,  also  certain,  added  to  income 
one  year  hence.  The  influence  of  risk  on  time-preference 
therefore  means  the  influence  of  uncertainties  in  the 
anticipated  income  of  an  individual  upon  his  relative 
valuation  of  present  and  future  small  increments  of  in- 
come, both  increments  being  certain.  The  manner  in 
which  risk  operates  upon  time-preference  will  differ  accord- 
ing to  the  particular  periods  in  the  future  to  which  the  risk 
applies.  If  the  possessor  of  income  regards  the  income 
of  the  immediate  future  as  fairly  well  assured,  but  fears  the 
loss  of  income  in  more  remote  periods,  he  may  be  aroused 
to  a  high  appreciation  of  the  needs  of  that  remote  future  and 
save  from  his  present  certain  abundance  in  order  to  provide 
for  the  later  possible  scarcity.  Income  in  which  this  sort 
of  risk  exists  tends,  therefore,  to  produce  a  low  rate  of 
time-preference  for  income  which  is  immediate  and  cer- 
tain as  compared  with  income  which  is  remote  and  uncer- 
tain. In  actual  fact,  such  a  type  is  not  uncommon.  The 
remote  future  is  usually  less  known  than  the  immediate 
future.  Tliis  means  that  the  risk  connected  with  distant 
income  is  greater  than  that  connected  with  income  near 
at  hand.  The  chance  of  disease,  accident,  disability,  or 
death  is  always  to  be  reckoned  with,  but  under  ordinary 
circumstances  is  greater  in  the  remote  future  than  in  the 
immediate  future.  Consequently  there  is  usually  a  ten- 
dency toward  a  low  time-preference.  Tliis  tendency  is 
expressed  in  the  phrase  to  "lay  up  for  a  rainy  day." 

But  the  influence  of  risk  is  not  always  in  the  direction  of 
lowering  time-preference.  Sometimes  the  relative  un- 
certainty is  reversed,  and  immediate  income  is  subject 
to  higher  risk  than  remote  income.  Such  is  the  case 
in  war  or  other  temporary  threat  of  misfortune.  Such  is 
also  the  case  when  an  individual  is  assured  a  permanent 
position  with  a  salary  after  a  certain  time,  but  in  the  mean- 


Sec.  8]  TIME-PREFERENCE  101 

time  must  obtain  a  precarious  subsistence.  In  these  cases 
the  effect  of  the  risk  element  is  to  enhance  the  estimation 
in  which  immediate  income  is  held.  Again  the  risk  may, 
instead  of  applying  especially  to  remote  periods  or  espe- 
cially to  immediate  periods,  apply  to  all  alike.  Such  a  con- 
dition largely  explains  why  salaries  and  wages  are  lower 
than  the  average  earnings  of  those  who  work  for  themselves. 
Tliose  who  choose  salaries  rather  than  profits  are  willing 
to  accept  a  low  income  in  order  to  get  rid  of  a  precarious 
one.  Since  a  risky  income,  if  the  risk  applies  evenly  to 
all  parts  of  the  income-stream,  is  nearly  equivalent  to 
a  low  income,  and  since  a  low  income,  as  we  have  seen, 
tends  to  create  a  high  time-preference,  risk,  if  uniformly 
distributed  in  time,  must  tend  to  raise  time-preference. 

We  see,  then,  that  risk  tends  in  some  cases  to  increase 
and  in  others  to  decrease  the  rate  of  time-preference.  But 
there  is  a  common  principle  in  all  these  cases.  Whether 
the  result  is  a  high  or  a  low  time-preference,  the  primary 
fact  is  that  the  risk  of  losing  the  income  in  a  particular  period 
of  time  operates  as  a  virtual  impoverishment  of  the  income 
in  that  period,  and  hence  increases  the  estimation  in 
which  it  is  held.  If  that  period  is  a  remote  one,  the  risk 
to  which  it  is  subject  makes  for  a  high  appreciation  of  re- 
mote income;  if  the  period  is  the  immediate  future,  the 
risk  makes  for  a  high  appreciation  of  immediate  income; 
if  the  risk  is  in  all  periods  of  time,  it  acts  as  a  virtual  de- 
crease of  income  all  along  the  line. 

There  are,  however,  anomalous  individuals  in  whom 
caution  is  absent  or  perverted.  Upon  these,  risk  will  have 
quite  the  opposite  effects.  Some  persons,  who  see  gi'eat 
speculative  chances  in  the  remote  future,  may  treat  that 
future  as  though  it  were  especially  well-endowed,  and  there- 
fore be  willing  to  sacrifice  a  large  amount  of  their  "great 
expectations"  in  the  future  for  the  sake  of  a  relatively 
small  addition  to  their  present  income.  In  other  words, 
they  will  have  a  high  time-preference.  The  same  individ- 
uals, if  receiving  an  income  which  is  risky  for  all  periods 


102  THE  RATE  OF  INTEREST  [Chap.  VI 

of  time  alike,  might  have,  as  a  result,  a  low  instead  of  a 
high  time-preference. 

The  income  to  which  risk  applies  may  be  either  the  in- 
come from  articles  of  capital  external  to  man,  or  the  income 
from  man  himself.  In  the  latter  case  the  risk  of  losing 
the  income  is  the  risk  of  death  or  invalidism.  This  risk  — 
the  micertainty  as  to  human  life  and  health  —  differs 
somewhat  from  the  uncertainty  of  income  dependent  on 
objective  capital ;  for  the  cessation  of  life  not  only  produces 
a  cessation  of  income  from  the  human  machine,  but  a  ces- 
sation of  the  enjoyment  of  all  income  whatsoever.  For 
persons  who  have  children  whose  future  welfare  they  have 
at  heart,  this  consideration  loses  much  of  its  force.  A  man 
with  wife  and  children  is  willing  to  pay  a  high  insurance 
premium  in  order  that  they  may  continue  to  enjoy 
an  income  after  his  death,  while  an  unmarried  man,  or 
a  man  who  cares  only  for  self-indulgence  and  wishes  to 
"make  the  day  and  the  journey  alike,"  will  not  try  to  con- 
tinue the  income  after  his  death.  Uncertainty  of  life  in  the 
latter  case  is  especially  calculated  to  produce  a  high  degree 
of  time-preference.  Sailors  offer  a  good  example.  They 
are  natural  spendthrifts,  and  when  they  have  money  use 
it  lavishly.  The  risk  of  shipwreck  is  constantly  before 
them,  and  their  motto  is,  "A  short  life  and  a  merry  one." 

The  effect  of  risk,  therefore,  is  manifold,  according  to  the 
degree  and  range  of  application  of  risk  to  various  periods 
of  time;  according  to  the  cautious  or  incautious  character 
of  the  individual;  according  to  whether  or  not  the  risk  in 
question  applies  to  human  life,  and  if  so,  according  to 
whether  or  not  the  individual's  interest  in  the  future  ex- 
tends beyond  his  own  lifetime.  The  manner  in  which 
these  tendencies  operate  upon  the  rate  of  interest  will  be 
discussed  in  Chapter  XI. 

§9 

The  proposition  that  the  preference  for  present  over 
future  income  depends  upon  the  income,  its  size,  time- 


Sec.  9]  TIME-PREFERENCE  103 

shape,  composition,  and  probability,  does  not  deny  that 
it  may  depend  on  other  factors  also,  just  as,  in  the  theory 
of  prices,  the  proposition  that  the  marginal  utility  of  an 
article  depends  upon  the  quantity  of  that  article  does  not 
deny  that  it  may  depend  on  other  elements  as  well.  But 
the  dependence  of  time-preference  on  income  is  of  most 
importance,  for  time-preference  is  a  preference  for  income. 
It  is  in  the  same  way  that  the  dependence  of  the  marginal 
utility  of  bread  on  the  quantity  of  bread  is  more  important 
than  its  dependence  on  the  quantity  of  some  other  com- 
modity, such  as  butter.  As  to  the  dependence  of  this  time- 
preference  for  income  on  other  factors  than  that  income, 
these  other  factors  may  conveniently  be  regarded  as  affect- 
ing the  "  form  of  the  function"  which  expresses  its  depend- 
ence on  income.  In  this  light  may  be  considered  the 
influence  of  "the  personal  equation."  It  is  clear  that  the 
rate  of  time-preference  which  corresponds  to  a  specific 
income-stream  will  not  be  the  same  for  everybody.  One 
man  may  have  a  time-preference  of  5  per  cent,  and  another 
10  per  cent.,  although  both  have  the  same  income.  The 
difference  will  be  due  to  the  personal  characteristics  of 
the  individuals.  These  characteristics  are  chiefly  five  in 
number :  ^  (1)  foresight,  (2)  self-control,  (3)  habit,  (4)  ex- 
pectation of  life,  (5)  interest  in  the  lives  of  other  persons. 
We  shall  take  these  up  in  order. 

(1)  First,  as  to  foresight.  Generally  speaking,  the  greater 
the  foresight,  the  less  the  rate  of  time-preference,  and  vice 
versa.''    In  the  case  of  primitive  races  and  uninstructed 


*  Cf.  Rae's  Sociological  Theory  of  Capital,  p.  54.  Also  Bohm- 
Bawerk,  The  Positive  Theory  of  Capital,  Book  V,  Chap.  III. 

^  To  be  exact,  we  should  observe  that  lack  of  fore.sight  may  either 
increase  or  decrease  time-preference.  Although  most  persons  who 
lack  foresight  err  by  failing  to  give  due  weight  to  the  importance  of 
future  needs,  or,  what  amounts  to  the  same  thing,  by  overestimating 
the  provision  existing  for  such  future  needs,  cases  are  not  lacking  in 
which  the  opposite  error  is  committed ;  that  is,  the  individual  exagger- 
ates the  needs  of  the  future  or  undere.stimates  the  provision  likely  to  be 
made  for  them.     In  order  not  to  complicate  the  text,  only  the  former 


104  THE  RATE  OF  INTEREST  [Chap.  VI 

classes  of  society,  the  future  is  seldom  considered  in  its 
true  proportions.  The  story  is  told  of  such  a  person  that 
he  would  not  mend  his  leaky  roof  when  it  was  raining,  for 
fear  of  getting  more  wet,  nor  when  it  was  not  raining,  be- 
cause he  did  not  then  need  shelter.  Among  such  persons, 
the  preference  for  present  gratification  is  powerful  because 
their  comprehension  of  the  future  is  weak.  In  regard  to 
foresight,  Rae  states :  ^  — 

"The  actual  presence  of  the  immediate  object  of  desire  in  the 
mind,  by  exciting  the  attention,  seems  to  rouse  all  the  faculties, 
as  it  were,  to  fix  their  view  on  it,  and  leads  them  to  a  very  Uvely 
conception  of  the  enjojTQents  which  it  offers  to  their  instant  pos- 
session. The  prospects  of  future  good,  which  future  years  may 
hold  out  to  us,  seem  at  such  a  moment  dull  and  dubious,  and  are 
apt  to  be  slighted,  for  objects  on  which  the  daylight  is  falling 
strongly,  and  showing  us  in  all  their  freshness  just  within  our  grasp. 
There  is  no  man,  perhaps,  to  whom  a  good  to  be  enjoyed  to-day, 
would  not  seem  of  very  different  importance,  from  one  exactly 
similar  to  be  enjoyed  twelve  years  hence,  even  though  the  arrival 
of  both  were  equally  certain." 

The  sagacious  business  man  represents  the  other  ex- 
treme; he  is  constantly  forecasting.  These  differences  in 
degrees  of  foresight  produce  corresponding  differences  in 
the  dependence  of  time-preference  on  the  character  of  in- 
come. Thus,  for  a  given  income,  say  $1000  a  year,  the 
reckless  might  have  a  time-preference  of  10  per  cent.,  when 
the  forehanded  would  experience  a  preference  of  only  5  per 
cent.  In  both  cases  the  preference  will  depend  on  the  size 
of  the  income,  being  higher  the  lower  the  income ;  but  the 
particular  rates  corresponding  to  a  particular  income  in 
the  two  cases  will  be  entirely  different.  Therefore  the 
rate  of  preference,  in  general,  will  be  higher  in  a  com- 
munity consisting  of  reckless  individuals  than  in  one 
consisting  of  the  opposite  type. 

and  more  common  error  will  be  hereafter  referred  to  when  "  lack  of  fore- 
sight" is  mentioned.    But  the  reader  may  in  each  such  case  readily 
add  the  possibility  of  the  contrary  error. 
'  Sociological  Theory  of  Capital,  p.  54. 


Sec.  9]  TIME-PREFERENCE  105 

(2)  We  come  next  to  self-control.  Tliis  trait,  though 
distinct  from  foresight,  is  usually  associated  with  it  and 
has  very  similar  effects.  Foresight  has  to  do  with  think- 
ing, self-control  with  willing.  A  weak  will  usually  goes 
with  a  weak  intellect,  though  not  necessarily,  and  not 
always.  The  effect  of  a  weak  will  is  similar  to  the  effect 
of  inferior  foresight.  Like  those  workingmen  who  cannot 
carry  their  pay  home  Saturday  night,  but  spend  it  on  the 
way  in  the  grogshop,  many  persons  cannot  deny  themselves 
any  present  indulgence,  even  when  they  know  definitely 
what  the  consequences  will  be  in  the  futiu^e.  Others,  on 
the  contrary,  have  no  difficulty  in  stinting  themselves  in 
the  face  of  all  temptations. 

(3)  The  third  characteristic  of  human  natui'e  which  needs 
to  be  considered  is  habit.  Tliat  to  which  one  is  accustomed 
exerts  necessarily  a  powerful  influence  upon  his  valuations 
and  therefore  upon  his  time-preference.  This  influence 
may  be  in  either  direction.  Rich  men's  sons,  accustomed 
to  the  enjoyment  of  a  large  income,  are  apt  to  put  a  higher 
valuation  on  present  compared  with  future  income  than 
would  persons  of  the  same  income  who  were  brought  up 
under  different  conditions.  If  they  suffer  a  reverse  of 
fortune,  they  find  it  harder  to  live  moderately  than  those 
of  equal  means  who  have  risen  instead  of  fallen  in  the 
economic  scale ;  and  this  will  be  true  even  if  foresight  and 
self-control  are  the  same  in  the  two  cases. 

(4)  The  fourth  circumstance  which  may  influence  the 
form  of  the  function  by  which  time-preference  depends  on 
the  character  of  income  has  to  do  with  the  imcertainty 
of  life  of  the  recipient  of  that  income.  We  have  already 
seen  in  a  different  connection  that  the  time-preference  of  an 
individual  will  be  affected  by  the  prospect  of  a  long  or  short 
life,  both  because  the  termination  of  life  brings  the  termina- 
tion of  the  income  from  lal^or,  and  because  it  also  ter- 
minates the  enjoyment  of  all  income.  It  is  the  latter  fact 
in  which  we  are  here  interested ;  the  expectation  of  life  af- 
fects the  dependence  of  time-preference  on  income.    There 


106  THE  RATE  OF  INTEREST  [Chap.  VI 

will  be  differences  among  different  classes,  different  indi- 
viduals, and  different  ages  of  the  same  individual.  So  far 
as  age  is  concerned,  the  usual  course  of  events  is  as 
follows:  The  time-preference  in  the  early  periods  of  life 
is  high  because  foresight  and  self-control  are  weak. 
Children  are  notorious  spendthrifts.  A  little  later,  when 
the  individual  has  acquired  some  self-control  and  fore- 
sight, he  will  still  have  a  high  rate  of  preference,  but 
for  another  reason,  —  the  prospect  of  an  ascending  in- 
come-stream. His  present  income  is  small,  but  he  looks 
forward  to  having  an  ample  income  in  five  or  ten  years. 
As  the  time  of  marriage  and  middle  life  approaches,  the 
opposite  tendency  may  assert  itself.  Foreseeing  the  needs 
of  middle  life  and  anticipating  no  increase  in  the  provision 
for  those  needs,  he  will  cease  to  borrow  and  begin  to  save. 
After  he  has  passed  middle  age,  when  his  children  have 
become  self-supporting,  and  he  looks  forward  to  de- 
clining years,  matters  are  reversed  again.  He  will  want 
to  enjoy  his  income  while  he  may,  the  income  beyond 
his  death  being  of  no  significance  to  him  except  as  it 
can  be  bequeathed  to  his  descendants.  The  prospect 
of  death  plays  an  important  role  in  the  thoughts  of 
the  old.  One  evidence  of  this  is  the  prominence  given 
to  it  in  all  philosophical  and  religious  systems.^  The 
philosophy  of  Horace,  for  instance,  was  summed  up  in  the 
maxim  "carpe  diem,"  which  is  practically  the  same  as 
the  still  older  maxim,  "eat,  drink,  and  be  merry,  for  to- 
morrow we  die."  Tlie  chance  of  death  may  be  said  to 
be  the  most  important  rational  factor  tending  to  make 
the  rate  of  time-preference  high,  and  anything  that  would 
tend  to  prolong  human  life  would  tend  at  the  same  time 
to  reduce  the  rate  of  time-preference.    As  Rae  says :  ^  — 

"Were  life  to  endure  forever,  were  the  capacity  to  enjoy  in  per- 
fection all  its  goods,  both  mental  and  corporeal,  to  be  prolonged 

'  See  MetchnikoflF,  Nature  of  Man,  English  translation,  New  York 
(Putnams),  1903,  Part  II. 

^  The  Sociological  Theory  of  Capital,  pp.  53-54. 


Sec.  9]  TIME-PREFERENCE  107 

with  it,  and  were  we  guided  solely  by  the  dictates  of  reason,  there 
could  be  no  limit  to  the  formation  of  means  for  future  gratification, 
till  our  utmost  wishes  were  supplied,  A  pleasure  to  be  enjoyed, 
or  a  pain  to  be  endured,  fifty  or  a  hundred  years  hence,  would  be 
considered  deserving  the  same  attention  as  if  it  were  to  befall 
us  fifty  or  a  hundred  minutes  hence,  and  the  sacrifice  of  a  smaller 
present  good,  for  a  greater  future  good,  would  be  readily  made,  to 
whatever  period  that  futurity  might  extend.  But  life,  and  the 
power  to  enjoy  it,  are  the  most  uncertain  of  all  things,  and  we  are 
not  guided  altogether  by  reason.  We  know  not  the  period  when 
death  may  come  upon  us,  but  we  know  that  it  may  come  in  a  few 
days,  and  must  come  in  a  few  years.  Why  then  be  providing 
goods  that  cannot  be  enjoyed  until  times,  which,  though  not  very 
remote,  may  never  come  to  us,  or  until  times  stUl  more  remote, 
and  which  we  are  convinced  we  shall  never  see?  If  life,  too,  is 
of  uncertain  duration  and  the  time  that  death  comes  between  us 
and  all  our  possessions  unknown,  the  approaches  of  old  age  are  at 
least  certain,  and  are  dulling,  day  by  day,  the  relish  of  every 
pleasure." 

The  shortness  of  life  thus  tends  powerfully  to  raise  the 
rate  of  time-preference.  This  is  especially  evident  when 
the  income-streams  compared  are  long.  A  lover  of  music 
will  prefer  a  piano  at  once  to  a  piano  available  next  year, 
because,  since  either  will  outlast  his  own  life,  he  will  get 
one  more  year's  use  out  of  the  piano  available  at  once. 

From  what  has  been  said  it  is  clear  that  there  are  three 
periods  in  his  life  when  a  man's  time-preference  is  espe- 
cially high :  (1)  in  early  life  it  is  high  because  of  youthful 
recklessness;  (2)  in  the  preparatory  stage,  because  future 
income  seems  relatively  abundant;  and  (3)  late  in  life, 
because  future  income  seems  relatively  superfluous. 

(5)  But  whereas  the  shortness  or  imcertainty  of  life  tends 
to  raise  the  rate  of  time-preference,  its  effect  is  greatly 
mitigated  by  the  fifth  circumstance,  the  care  for  the  welfare 
of  posterity.  Probably  the  most  powerful  cause  tending  to 
reduce  the  rate  of  interest  is  the  love  of  one's  children  and 
the  desire  to  provide  for  their  good.  When  these  sentiments 
decay,  as  they  did  at  the  time  of  the  decline  and  fall  of  the 
Roman  Empire,  and  the  fashion  is  to  exliaust  wealth  in 


108  THE  RATE  OF  INTEREST  [Chap.  VI 

self-indulgence  and  leave  little  or  nothing  to  offspring, 
the  rate  of  time-preference  and  rate  of  interest  will  be 
high.  At  such  times  the  motto,  "After  us  the  deluge," 
indicates  the  feverish  desire  to  squander  in  the  present,  at 
whatever  cost  to  the  future/ 

In  a  community  like  the  United  States,  where  parents 
regard  their  lives  as  continuing  after  death  in  the  lives  of 
their  children,  there  exists  a  high  appreciation  of  the  needs 
of  the  future  which  tends,  therefore,  to  produce  a  low  rate  of 
time-preference.  It  is  this  sentiment  which  is  responsible 
for  the  enormous  extension  of  life  insurance.  At  present 
in  the  United  States  the  insurance  on  lives  amounts  to 
$20,000,000,000.  This  represents,  for  the  most  part,  an 
investment  of  the  present  generation  for  the  next.  The 
investment  of  this  sum  springs  out  of  a  low  time-preference, 
and  tends  to  produce  a  low  rate  of  interest. 

Not  only  does  the  regard  for  posterity  lower  interest,  but 
the  increase  of  posterity  has  in  part  the  same  effect.  So 
far  as  an  increase  in  the  size  of  a  family  reduces  the  income 
per  capita  of  that  family,  it  operates,  like  impoverishment, 
to  increase  time-preference.  So  far  as  it  adds  to  future 
needs  rather  than  to  immediate  needs,  it  operates,  hke  a 
descending  income-stream,  to  diminish  time-preference. 
Parents  with  large  families  feel  the  importance  of  providing 
for  future  years  far  more  than  parents  otherwise  similar  but 
with  small  families.  Tliey  try  harder  to  save  and  to  take  out 
life  insurance.  In  other  words,  their  rate  of  preference 
for  present  over  future  income  is  lowered.  An  increase  of 
population,  therefore,  will,  other  things  being  equal,  reduce 
the  rate  of  interest.  This  proposition  must  not  be  thought 
to  conflict  with  the  reciprocal  proposition  that  the  same 
prudent  regard  for  the  future  which  is  created  by  the  re- 
sponsibilities of  parenthood  itself  tends  to  diminish  the 
number  of  offspring.  An  increase  of  population  tends 
toward    a   low    time-preference,    but   reciprocally   a   low 

'  See  Rae,  The  Sociological  Theory  of  Capital,  p.  97. 


Sec.  10]  TIME-PREFERENCE  109 

time-preference  tends  to  check  such  increase.  Hence  it  is 
that  the  thrifty  Frenchman  and  Scotchman  have  small 
families. 

§  10 

Time-preference,  therefore,  depends  for  each  individual 
on  his  income;  that  is,  its  size,  time-shape,  composition, 
and  probability;  but  the  jottti  of  this  dependence  differs 
according  to  the  various  circumstances  of  the  individual. 
The  circumstances  which  will  tend  to  make  his  time- 
preference  high  are  (1)  shortsightedness,  (2)  a  weak  will, 
(3)  the  habit  of  spending  freely,  (4)  the  shortness  and 
uncertainty  of  his  life,  (5)  selfishness,  or  the  absence  of  any 
desire  to  provide  for  posterity.  Tlie  reverse  conditions 
will  tend  to  make  his  rate  of  preference  low;  namely, 
(1)  a  high  degree  of  foresight,  which  enables  him  to  give 
to  the  future  such  attention  as  it  deserves;  (2)  a  high 
degree  of  self-control,  which  enables  him  to  abstain  from 
present  income  in  order  to  increase  future  income;  (3) 
the  habit  of  thrift;  (4)  the  probability  of  long  life;  (5) 
the  possession  of  a  family  and  a  high  regard  for  their 
welfare  after  his  death. 

The  resultant  of  these  various  tendencies  in  any  one  in- 
dividual will  determine  the  degree  of  his  time-preference 
in  relation  to  any  'particular  income.  This  result  will  differ 
as  between  individuals,  and  as  between  different  times  for 
the  same  individual.  The  essential  fact,  however,  is  that 
for  any  given  individual  at  any  given  time,  his  time-prefer- 
ence depends  in  a  definite  manner  upon  the  size,  shape, 
composition,  and  probability  of  his  income-stream. 

§  11 

This  view,  that  the  rate  of  time-preference  and  conse- 
quently the  rate  of  interest  depend  upon  income,  needs 
to  be  contrasted  with  the  common  view,  which  makes  the 


110  THE  RATE  OF  INTEREST  [Chap.  VI 

rate  of  interest  depend  merely  on  the  scarcity  or  abundance 
of  capital.  It  is  commonly  believed  that  where  capital  is 
scarce,  interest  is  high,  and  where  capital  is  plentiful,  in- 
terest is  low.  In  a  general  way  there  is  undoubtedly  some 
truth  in  this  proposition ;  and  yet  it  contains  a  misinterpre- 
tation of  borrowing  and  lending.  It  is  true  that  when  and 
where  men  are  anxious  to  lend,  interest  is  low,  and  when 
and  where  men  are  anxious  to  borrow,  interest  is  high. 
But  it  is  not  true  that  the  more  capital  a  man  has  the  more 
anxious  he  is  to  lend,  and  the  less  capital  he  has  the  more 
anxious  he  is  to  borrow.  The  willingness  to  lend  or  bor- 
row depends  primarily,  not  upon  the  amount  of  one's 
capital,  but  upon  the  character  of  the  income  which  he 
gets  from  it,  —  whether  this  income  is  large  or  small,  im- 
mediate or  deferred,  of  what  elements  it  consists,  whether 
it  is  certain  or  uncertain. 

The  proposition  that  abundance  of  capital  tends  to 
lower  interest  is  thus  very  superficial;  for  abundant 
capital  merely  means  abundant  income.  Capital-value  is 
discounted  income.  Behind,  or  rather  beyond,  a  capital 
of  $100,000  is  the  income  which  that  capital  represents. 
To  fix  attention  on  the  $100,000  capital  instead  of  on 
the  income  is  to  use  the  capital  as  a  cloak  to  cover  up 
the  real  factor  in  the  case.  Moreover,  capital-value  is 
itself  dependent  on  the  rate  of  interest.  The  capital- value 
of  a  farm  will  be  doubled  if  the  rate  of  interest  is  halved. 
In  such  a  case  there  would  be  found  more  capital  in 
farms ;  for  the  farms  in  a  community  would  rise,  say,  from 
$10,000,000  to  $20,000,000.  But  it  is  not  the  rise  in  cap- 
ital which  produces  the  fall  in  interest.  On  the  contrary, 
it  is  the  fall  in  the  interest  rate  which  produces  the  rise  in 
the  valuation  of  capital.  If  we  attempt  to  make  the  rate  of 
interest  depend  on  capital-value,  then,  since  capital-value 
depends  on  two  factors,  —  the  prospective  income  and  the 
rate  of  interest,  —  we  thereby  make  the  interest  rate  depend 
partly  on  income  and  partly  on  itself.  The  dependence 
on  itself  is  of  course  nugatory,  and  we  are  brought  back  to 


Sec.  11]  TIME-PREFERENCE  HI 

its  dependence  on  income  as  the  only  fact  of  real  signifi- 
cance. 

But  even  as  thus  amended  and  explained,  the  proposition 
that  the  rate  of  interest  depends  on  the  amount  of  capital 
is  not  satisfactory.  The  mere  amount  of  capital  does  not 
tell  us  much  about  the  income  for  which  that  capital  stands. 
To  know  that  one  man  has  a  capital  worth  $100,000,  and 
another  $200,000,  shows,  to  be  sure,  that  the  latter  man 
may  have  an  income  of  double  the  value  of  the  former;  but 
it  tells  us  absolutely  nothing  as  to  the  "time-shapes"  of 
the  two  incomes;  and  the  time-shape  of  income  has,  as 
we  have  seen,  a  most  profound  influence  on  the  time- 
preference  of  its  possessor. 

Let  us  suppose  two  communities  similar  in  population, 
distribution  of  wealth,  and  all  other  particulars  except  in 
the  amount  of  their  capital  and  the  character  of  the  income 
which  that  capital  represents.  One  of  these  two  communi- 
ties we  shall  suppose  has  a  capital  of  $100,000  invested,  as 
in  Nevada,  in  mines  and  quarries  nearly  exhausted,  while 
in  the  other  community  there  is  $200,000  of  capital  invested 
in  young  orchards  and  forests,  as  in  Florida.  According 
to  the  theory  that  abundance  of  capital  makes  interest  low, 
we  should  expect  the  Nevada  community  to  have  a  high 
rate  of  interest  compared  with  the  Florida  community. 
But  it  is  evident  that,  unless  other  circumstances  should 
interfere,  the  opposite  would  be  the  case ;  for  Nevada  has 
to  contemplate  a  decreasing  future  income,  and  in  order  to 
offset  the  depreciation  of  capital  which  follows  from  this 
condition,*  she  would  be  seeking  to  lend  or  invest  part  of 
the  income  of  the  present  or  immediate  future,  in  the  hope 
of  offsetting  the  decreased  product  of  the  mines  in  the  more 
remote  future.  The  Florida  planters,  on  the  contrary,  would 
be  inclined  to  borrow  against  their  future  crops.  If  the  two 
communities  are  supposed  to  be  commercially  connected, 
it  would  be  Nevada  which  would  lend  to  Florida,  notwith- 
standing the  fact  that  the  lending  community  was  the 

^  See  The  Nature  of  Capital  and  Income,  Chap.  XIV. 


112  THE  RATE  OF  INTEREST  [Chap.  VI 

poorer  in  capital  of  the  two.  From  the  illustration  it  is 
clear  that  the  mere  amount  of  capital-value  is  not  only 
a  misleading  but  a  very  inadequate  criterion  of  the  rate  of 
interest/ 

Apologists  for  the  common  statement  that  abundance 
or  scarcity  of  capital  lowers  or  raises  interest  might  be  in- 
clined to  argue  that  it  is  not  the  total  capital,  but  only  the 
"loanable  capital"  which  should  be  included,  and  that  the 
Nevada  community  had  more  "loanable  capital"  than  the 
Florida  community.  But  the  phrase  "loanable  capital" 
is  merely  another  cloak  to  cover  the  fact  that  it  is  not 
the  amount  of  capital,  but  the  decision  to  lend  or 
borrow  it,  which  is  important.  To  give  this  proposition 
meaning,  "loanable  capital"  must  be  taken,  not  in  the 
literal  sense  of  capital  which  can  be  lent,  —  for  all  capital 
is  loanable  in  this  sense ;  but  in  the  sense  of  capital  which 
persons  are  willing  to  lend.  Hence,  to  state  that  in  any 
community  there  is  abundance  of  loanable  capital  is  merely 
to  state  that  there  is  in  that  community  a  willingness  to 
lend  a  great  deal  of  capital.  Consequently,  the  proposition 
that  the  rate  of  interest,  or  preference  for  present  over 
future  goods,  is  low  when  loanable  capital  is  abundant 
becomes  reduced  to  the  platitude  that  the  rate  of  preference 
for  present  over  future  goods  is  low  when  men  wish  to  lend. 

But  it  may  be  said,  surely  in  a  money  market  there  exists 
at  one  time  a  large  visible  supply  of  loanable  money  and  at 
another  time  a  small  visible  supply,  and  this  supply  affects 
the  rate  of  interest.  This,  again,  is  a  true  but  a  superficial 
statement.  A  little  examination  will  show  that  the  abun- 
dance or  shortage  of  loanable  bank  funds  is  merely  a 
measure  of  the  decision  of  merchants  to  discount  or  deposit,  — 
in  other  words,  to  borrow  or  lend, — and  does  not  give  us  any 
clew  as  to  the  reason  why  they  do  so.     The  money  or  credit 

'  One  of  the  few  defects  in  Rae's  analysis  of  interest  is  his  em- 
phasis on  the  accumulation  of  capital.  Since  this  accumulation  is 
merely  in  anticipation  of  future  income,  the  emphasis  belongs  on  the 
latter. 


Sec.  12]  TIME-PREFERENCE  113 

is,  of  course,  the  mere  vehicle  by  which  the  bank  acts  as  an 
intermediary  or  broker  between  borrowers  and  lenders,  and 
does  not  represent  any  independent  factor  in  the  case. 

We  end,  therefore,  by  emphasizing  anew  the  importance 
of  fixing  our  eyes  on  income  and  not  on  capital.  It  is  only 
as  we  look  through  capital-value,  beyond  to  the  income 
which  it  represents,  that  we  reach  the  efficient  causes  which 
operate  upon  the  rate  of  interest.  The  absence  hitherto  of 
a  definite  theory  and  conception  of  income  has  prevented 
economists  from  doing  this.  Borrowing  and  lending  are 
in  form  a  transfer  of  capital,  but  they  are  in  fact  a  transfer 
of  income  of  which  that  capital  is  merely  the  present 
value.  In  our  theory  of  interest,  therefore,  we  have  to 
consider  not  primarily  the  amount  of  capital  of  a  com- 
munity, but  the  income  for  which  that  capital  stands. 

§  12 

Unfortunately  for  purposes  of  exposition,  the  relation 
between  time-preference  and  income  cannot  be  expressed 
in  a  simple  schedule  or  cm-ve,  as  can  the  relation  between 
demand  and  price,  or  supply  and  price,  or  utility  and  quan- 
tity consumed,  for  the  reason  that  income  means  not  a 
single  magnitude  merely,  but  a  conglomeration  of  a  number 
of  magnitudes.  As  mathematicians  would  express  it,  to 
state  that  time-preference  depends  on  the  character  of 
income,  its  size,  shape,  composition,  and  probability,  is 
to  state  that  time-preference  is  a  function  of  all  the 
different  magnitudes  which  need  to  be  specified  in  a  com- 
plete description  of  that  income.  A  geometrical  represen- 
tation, therefore,  of  the  dependence  of  time-preference  on 
the  various  magnitudes  which  characterize  income,  would 
be  impossible.  For  a  curve  can  only  represent  the  depend- 
ence of  a  magnitude  on  one  independent  variable;  even 
a  surface  can  onl}^  represent  dependence  on  two;  but  for 
our  requirements  we  should  need  a  space  of  n  dimensions. 
We  may  represent  the  relation  between   time-preference 


114  THE  RATE  OF  INTEREST  [Chap.  VI 

and  income  by  a  "schedule"  like  the  ordinary  "demand 
schedule"  and  "supply  schedule,"  if  we  make  a  list  of  all 
possible  incomes,  specifying  for  each  individual  income  all 
its  characteristics,  —  its  size,  time-shape  (that  is,  its  relative 
magnitude  for  each  successive  time-interval  considered),  its 
composition  (or  the  amount,  at  each  period,  of  each  in- 
dividual constituent,  as  nourishment,  shelter,  etc.),  and 
the  certainty  or  uncertainty  attached  to  all  these  elements. 
Having  thus  compiled  a  list  of  all  possible  incomes,  it  would 
only  be  necessary  for  us  to  assign  to  each  of  them  the  rate  of 
time-preference  pertaining  to  it.  Such  a  schedule  would 
be  too  complicated  and  cumbersome  to  carry  out  in  detail ; 
but  the  following  will  roughly  indicate  some  of  the  main 
groups  of  which  it  would  consist.  In  this  schedule  we  have 
represented  by  the  three  vertical  lines  three  different  classes 
of  income,  —  two  extreme  types  and  one  mean  type,  —  so 
that  the  corresponding  rates  of  time-preference  range  them- 
selves in  a  descending  series  of  numbers.  We  have  also 
represented  by  the  three  vertical  columns  three  different 
classes  of  individuals,  two  being  of  extreme  types  of  in- 
dividuals, and  the  third  of  a  mixed  or  medium  type.  Thus 
the  numbers  in  the  table  descend  as  we  proceed  either 
down  or  toward  the  right,  the  lowest  number  of  all  being 
in  the  lower  right-hand  corner. 


Sbc.  12] 


TIME-PREFERENCE 


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116  THE  RATE  OF  INTEREST  [Chap.  VI 

Out  of  the  large  number  of  possible  incomes  represented 
in  such  a  schedule,  of  course  only  one  can  be  the  actual 
income  of  the  individual.  The  one  which  exists  in  any 
case  is  to  a  large  extent  a  matter  of  choice,  as  we  shall  see 
in  the  next  chapter.  Since  time-preference  may  be  varied 
by  voluntarily  varying  the  character  of  the  income-stream 
on  which  it  depends,  it  follows  that  the  shortsighted,  weak- 
willed  spendthrift  individual  may  not  have,  as  a  matter  of 
fact,  any  higher  rate  of  time-preference  than  his  farsighted, 
self-controlled,  abstemious  brother.  In  fact,  where  a  loan 
market  is  in  full  operation,  the  tendency  is  for  the  two  in- 
dividuals to  select  such  income-streams  as  will  bring  their 
time-preference  into  unison.  How  this  is  accomplished 
will  form  the  subject  of  the  following  chapter. 


CHAPTER  VII 

FIRST  APPROXIMATION  TO   THE   THEORY   OF   INTEREST 
(assuming   INCOME   RIGID) 

§    1 

In  the  last  chapter  we  saw  that  the  rate  of  preference  for 
present  over  future  goods  was,  in  the  last  analysis,  a  prefer- 
ence for  present  over  future  income;  that  this  preference 
depends,  for  any  given  individual,  upon  the  character  of  his 
income-stream,  —  its  size,  time-shape,  composition,  and 
probability,  —  and  that  the  nature  of  this  dependence  varies 
with  different  individuals.  The  question  at  once  arises, 
will  not  the  rates  of  preference  of  different  individuals  be 
very  different,  and  if  so,  what  relation  do  these  different 
rates  have  to  the  rate  of  interest?  John  Rae  assumed  that 
the  rates  differed  widely,  and  that  the  rate  of  interest  was 
a  sort  of  average  of  their  different  magnitudes.  But  this  is 
incorrect.  In  a  nation  of  hermits,  in  which  there  was  no 
mutual  lending  and  borrowing,  the  time-preferences  of 
individuals  would  diverge  widely;  but  in  modern  society, 
borrowing  and  lending  tend  to  bring  into  equality  the  rates 
of  preference  in  different  minds.  It  is  only  because  of 
the  limitations  of  the  loan  market  that  absolute  equality 
is  not  reached. 

The  chief  limitation  to  lending  is  due  to  the  risk  involved, 
and  to  the  difficulty  or  impossibility  of  obtaining  the  se- 
curity necessary  to  eliminate  or  reduce  that  risk.  Those 
who  are  most  willing  to  borrow  are  oftentimes  those  who 
are  least  able  to  give  security.  It  will  then  happen  that 
these  persons,  shut  off  from  the  loan  market,  experience  a 
higher  rate  of  time-preference  than  the  rate  of  interest  ruling 

117 


118  THE  RATE   OF  INTEREST  [Chap.  VII 

in  that  market.  If  they  can  contract  loans  at  all,  it  will 
be  only  through  the  pawn  shop  or  other  high-rate  agencies. 
But,  for  the  moment,  let  us  assume  a  perfect  market, 
in  which  the  element  of  risk  is  entirely  lacking,  both  with 
respect  to  the  certainty  of  the  expected  income-streams 
belonging  to  the  different  individuals,  and  with  respect  to 
the  certainty  of  repayment  for  loans.  In  other  words,  we 
assume  that  each  individual  is  initially  possessed  of  a  fore- 
known income-stream,  and  that  he  is  free  to  exchange 
any  part  of  it  to  some  other  person,  in  consideration  of 
receiving  back  at  some  future  time  an  addition  to  his  in- 
come for  the  prospective  period.  We  assume  further  that 
to  buy  and  sell  various  parts  of  his  income-stream  (by 
loans,  etc.),  is  his  only  method  of  altering  that  income- 
stream.  Prior  to  such  exchange,  his  income-stream  is 
rigid,  i.e.  fixed  in  size,  time-shape,  and  composition.  The 
capital-instruments  which  he  possesses  are  each  capable 
of  only  a  single  definite  series  of  services  contributing  to 
his  income-stream.  These  assumptions  that  each  man's 
income-stream  is  initially  certain  and  fixed,  will  be  used  in 
our  first  approximation  to  the  theory  of  interest. 

§  2 

Under  these  hypothetical  conditions,  the  rates  of  time- 
preference  for  different  individuals  would  be  perfectly 
equalized.  Borrowing  and  lending  evidently  affect  the 
time-shape  of  the  incomes  of  borrower  and  lender;  and 
since  the  time-shape  of  their  incomes  affects  their  time- 
preference,  such  a  modification  of  time-shape  will  react 
upon  and  modify  their  time-preference,  and  bring  the 
market  into  equilibrium. 

If,  for  any  particular  individual,  the  rate  of  preference 
differs  from  the  market  rate,  he  will,  if  he  can,  adjust  the 
time-shape  of  his  income-stream  so  as  to  harmonize  his  pref- 
erence rate  with  the  interest  rate.  Those  who,  for  a  given 
income-stream,  have  a  rate  of  preference  above  the  market 


Sec.  2]  FIRST  APPROXIMATION  119 

rate,  will  sell  some  of  their  surplus  future  income  to  obtain 
an  addition  to  their  present  meager  income.  This  will  have 
the  effect  of  enhancing  the  value  of  the  future  income  and 
decreasing  that  of  the  present.  The  process  will  continue 
until  the  rate  of  preference  of  this  individual  is  equal  to 
the  rate  of  interest.  In  other  words,  a  person  whose 
preference  rate  exceeds  the  current  rate  of  interest  will 
borrow  up  to  the  point  which  will  make  the  two  rates  equal. 
Reversely,  those  who,  with  a  given  income-stream,  have  a 
preference  rate  below  the  market  rate,  will  sell  some  of  their 
abundant  present  income  to  eke  out  the  future,  the  effect 
being  to  increase  their  preference  rate  imtil  it  also  harmo- 
nizes with  the  rate  of  interest. 

To  put  the  matter  in  figures,  let  us  suppose  the  rate  of 
interest  is  5  per  cent.,  whereas  the  rate  of  preference  of  a 
particular  individual  is  10  per  cent.  Then,  by  hypothesis, 
the  individual  is  willing  to  sacrifice  $1.10  of  next  year's 
income  in  exchange  for  $1  of  this  year's.  But  in  the 
market  he  is  able  to  obtain  $1  for  this  year  by  spending  only 
$1.05  of  next  year.  This  ratio  is,  to  him,  a  cheap  price. 
He  therefore  borrows,  say,  $100  for  a  year,  agreeing  to 
return  $105;  that  is,  he  contracts  a  loan  at  5  per  cent, 
when  he  is  willing  to  pay  10  per  cent.  This  operation, 
by  increasing  his  present  income  and  decreasing  his  future, 
tends  to  reduce  his  time-preference  from  10  per  cent,  to, 
say,  8  per  cent.  Under  these  circumstances  he  will  borrow 
another  $100,  being  willing  to  pay  8  per  cent.,  but  having 
to  pay  only  5  per  cent.  This  operation  will  still  further 
reduce  his  time-preference,  until  it  has  been  finally  brought 
down  to  5  per  cent.  Then,  for  the  last  or  "marginal" 
$100,  his  rate  of  time-preference  will  agree  with  the  market 
rate  of  interest.  As  in  the  general  theory  of  prices,  this 
marginal  rate,  5  per  cent.,  being  once  established,  applies 
indifferently  to  all  his  valuations  of  present  and  future  in- 
come. Every  comparative  estimate  of  present  and  future 
which  he  actually  makes  must  be  "on  the  margin"  of  his 
income-stream  as  actually  determined.     The  above-men- 


120  THE  RATE  OF  INTEREST  [Chap.  VII 

tioned  10  per  cent,  and  8  per  cent,  rates  are  not  actually 
experienced  by  him  ;  they  merely  mean  the  rates  of  prefer- 
erence  which  he  would  have  experienced  had  his  income 
not  been  transformed  to  the  time-shape  correspondent  to 
5  per  cent. 

In  like  manner,  if  another  individual,  entering  the  loan 
market  from  the  other  side,  has  a  rate  of  preference  of 
2  per  cent.,  he  will  become  a  lender  instead  of  a  borrower. 
He  will  be  willing  to  accept  $102  of  next  year's  income  for 
$100  of  this.  But  in  the  market  he  is  able,  instead  of  the 
$102,  to  get  $105.  As  he  can  lend  at  5  per  cent,  when  he 
would  gladly  do  so  at  2  per  cent.,  he  jumps  at  the  chance 
and  invests,  not  one  $100  only,  but  another  and  another. 
But  his  present  income,  being  reduced  by  the  process,  is 
now  more  highly  esteemed  than  before,  and  his  future 
income,  being  increased,  is  less  highly  esteemed.  The  result 
will  be  a  higher  relative  valuation  of  the  present,  which, 
under  the  influence  of  successive  additions  to  the  sums  lent, 
will  rise  gradually  to  the  level  of  the  market  rate  of  interest. 

In  such  an  ideal  loan  market,  therefore,  where  every  in- 
dividual could  freely  borrow  or  lend,  the  rates  of  preference 
for  present  over  future  income  for  all  the  different  indi- 
viduals would  become  equal  to  each  other  and  to  the  rate 
of  interest, 

§  3 

To  illustrate  this  reasoning  by  a  diagram,  let  us  suppose 
the  income-stream  to  be  represented  as  in  Figure  6,  and  that 
the  possessor  wishes  to  obtain  a  small  item  X'  of  imme- 
diately ensuing  income,  for  a  somewhat  larger  item  X" 
later  on.  He  therefore  modifies  his  income-stream  from 
ABCD  to  EBD.  But  this  change  will  evidently  produce 
a  change  in  his  time-preference.  If  the  rate  of  time-pref- 
erence corresponding  to  the  income-stream  represented  by 
the  unbroken  line  is  10  per  cent.,  the  rate  of  preference  cor- 
responding to  the  broken  line  will  be  somewhat  less,  say 


Sec.  3] 


FIRST  APPROXIMATION 


121 


8  per  cent.  If  the  market  rate  of  interest  is  5  per  cent., 
it  is  evident  that  the  person  will  proceed  to  still  further 
borrowing.     By  repeating  the  operation  several  times  he 


A 


Fig.  6. 


can  evidently  produce  almost  any  required  conformation 
in  his  income-stream.  If,  instead  of  borrowing,  he  wishes 
to  lend  (Fig.  7),  he  surrenders  from  his  present  income- 


A 
E 


Fio.  7. 


stream  the  amount  X'  for  the  sake  of  the  larger  amount 
X"  at  a  later  time.  He  will  engage  in  the  former  series 
of  operations  if,  at  the  start,  his  subjective  preference 
for  present  goods  exceeds  the  market  rate  of  interest, 
and  in  the  latter,  if   it   falls  short  of  that  rate.      After 


122 


THE  RATE  OF  INTEREST 


[Chap.  VII 


Fia.  8. 


the  operations  are  completed  and  the  final  conformations 
of  the  income-streams  are  determined,  the  rates  of  time- 
preference  are  all  brought  into  conformity  with  the  market 
rate  of  interest. 

The  loan  is  effected  under  the  guise  of  money.     We  do 

not  confessedly  borrow  and 
lend  incomes,  but  money.  Yet 
money  —  that  universal  me- 
dium in  practice  and  universal 
stumbhng-block  in  theory 
—  merely  represents  capitalized  income.  A  hundred  dol- 
lars mean  the  power  to  secure  income,  —  any  income  the 
present  value  of  which  is  $100.  , 
When,     therefore,     a     person       ''"^^^ 

"borrows"    $100    to-day    and  A ""^^^ -B 

returns  $105  next  year,  in  ac-  """"- — B' 

tual   fact  he  secures  the    title  Fig.  9. 

to  $100  worth  of  future  income  —  immediately  future, 
perhaps  —  and  parts  with  the  title  to  $105  worth  of  income 
more  remotely  future. 

There  are  six  principal  types  of  individuals  in  a  loan 


A' 


Fig.  10. 


market.  In  the  first  type 
(Fig.  8)  the  individual  is  sup- 
posed to  be  possessed  of  an  in- 
creasing income-stream  AB 
which  in  his  mind  results  in 
a  rate  of  preference  above 
the  market  rate.  This  leads 
him  to  borrow,  and  relatively 
to  level  up  his  ascending  income-stream  to  such  a  position 
as  A'B'.  The  second  type  of  individual  already  possesses 
a  uniform  income-stream  AB  (Fig.  9),  but,  nevertheless, 
being  of  a  spending  type,  experiences  a  rate  of  preference 
also  above  the  market  rate,  and  will  therefore  modify  his 
income-stream  to  the  curve  A'B'.  The  third  type  is  rep- 
resented in  Figure  10.  This  individual  has  a  rate  of  pref- 
erence in  excess  of  the  market  rate,  even  with  a  descending 


Sbc.  3] 


FIRST  APPROXIMATION 


123 


y 


B' 


B 


curve  AB.  The  consequence  is  that  by  borrowing  he 
obtains  a  curve  A'B'  of  still  steeper  descent. 

The  preceding  three  cases  are  of  borrowers.     In  like  man- 
ner there  are   three   types   of     • 
lenders.      Figure  11  represents 

a  descending  type  of  income   a' _^^.,^ b' 

AB  which,  by  lending  present 

income    in    return  for   future  -v  ^ 

income,   is    converted    into  a  Fig.  ii. 

relatively  uniform  income  A'B'  \  Figure  12  represents  a 
uniform  income  converted,  by  lending,  into  an  ascend- 
ing income;  and  Figure  13  an  ascending  income  converted 
into  a  still  more  steeply  ascending  income. 

In  all  cases  we  see  that  the  borrowers  change  their  income 
curve  by  tipping  it  down  in  the  future  and  up  in  the  present ; 

whereas  the  lenders  tip  their 
income  curves  in  the  opposite 
direction.  Of  the  three  types 
of  borrowers  and  of  lenders, 
the  first  in  each  group  of  three 
(see  Figs.  8  and  11)  is  the 
usual  and  normal  case.  In  both  these  cases  the  effort  is 
to  transform  the  given  income  into  a  more  uniform  one, 
the  rising  curve  (Fig.  8)  being  lowered  and  the  falling 
curve  (Fig.  11)  being  raised  toward  a  common  horizontal 
position.  Figure  10  and  Figure  13,  on  the  other  hand, 
represent  extreme  and  unusual 
cases.  The  former  (Fig.  10) 
typifies  the  spendthrift  who, 
in  spite  of  lessening  income, 
borrows,  and  the  latter  (Fig. 
13)  typifies  the  miser  who,  in 
spite  of  rapidly  increasing  in- 
come, saves  even  more. 

But  whatever  the  personal  equation,  it  remains  true  that, 
for  each  individual,  the  more  ascending  his  income  curve 
the  higher  his  rate  of  preference,  and  the  more  descending 


Fig.  12. 


.b' 


a' 

A  " 


Fig.  13. 


124  THE  RATE  OF  INTEREST  [Chap.  VII 

the  curve,  the  lower  the  rate.  If  the  descent  is  sufficiently 
rapid,  the  rate  of  preference  could  be  made  zero  or  even 
negative.  In  these  cases,  the  income  is  such  that  its 
possessor  would  sacrifice  present  income  to  future,  even  if 
the  market  rate  of  interest  were  zero.^ 

These  are,  of  course,  not  the  only  types  which  could  be 
considered,  but  they  are  some  of  the  most  important.  To 
them  we  may  add  the  type  of  fluctuating  income,  as  rep- 
resented in  Figure  14,  which  may  result  in  alternate  bor- 


FiG.  14. 

rowing  and  lending  so  as  to  produce  a  more  nearly  uniform 
income-stream. 

It  must  not  be  imagined  that  the  classes  of  borrowers  and 
lenders  correspond  respectively  with  the  classes  of  poor 
and  rich.  Personal  and  natural  idiosyncracies,  early 
training  and  acquired  habits,  accustomed  style  of  living, 
the  usages  of  the  country,  and  other  circumstances  dis- 
cussed in  Chapter  VI,  will,  by  influencing  foresight,  self- 
control,  regard  for  posterity,  etc.,  determine  whether  a 
man's  rate  of  preference  is  high  or  low,  and  therefore 
whether  he  becomes  a  spender  or  a  saver.  So  far  as  the 
character  of  the  income-stream  itself  tends  to  place  an 
individual  in  one  or  the  other  of  these  classes,  the  nature  of 
the  influence  is  in  accordance  with  the  principles  stated  in 
Chapter  VI  in  respect  to  the  four  features,  size,  time-shape, 
composition,  and  probability.  As  to  size,  the  larger  the 
income  the  more  likely,  in  general,  is  its  possessor  to  become 
a  lender,  because  large  incomes,  in  general,  reduce  the  rate 
of  preference  for  present  over  future  income;   as  to  time- 

*  This  is  the  case  mentioned  by  Carver  {Theory  of  Distribution, 
pp.  232-236),  when  he  remarks  that  a  man  with  $100  in  his  pocket 
would  not  think  of  spending  it  all  on  a  dinner  to-day,  but  would  save 
at  least  some  of  it  for  to-morrow. 


Sec.  4]  FIRST   APPROXIMATION  125 

shape,  ascending  incomes  are  apt  to  make  the  possessors 
borrowers,  and  descending  incomes  to  make  them  lenders; 
as  to  composition,  incomes  well  endowed  with  the  food 
element  are  less  apt  to  make  their  possessors  borrowers 
than  incomes  of  the  contrary  type ;  and  as  to  probability, 
incomes  which  are  uncertain  tend  sometimes  to  make 
their  possessors  borrow,  sometimes  to  lend. 

§  4 

But  borrowing  and  lending  are  not  the  only  w^ays  in  which 
one's  income-stream  may  be  modified.  The  same  result 
may  be  accomplished  simply  by  buying  and  selling  property ; 
for,  since  property  rights  are  merely  rights  to  particular  in- 
come-streams, their  exchange  substitutes  one  such  stream  for 
another  of  equal  value  but  differing  in  time-shape,  composi- 
tion, or  certainty.  This  method  of  modifying  one's  income- 
stream,  which  we  shall  call  the  method  of  sale,  really  includes 
the  former  method  of  loan ;  for  a  loan  contract  is  at  bottom 
a  sale,  as  Bohm-Bawerk  has  so  clearly  shown.  Tliat  is, 
it  is  the  exchange  of  the  right  to  present  or  immediately 
ensuing  income  for  the  right  to  more  remote  or  future  in- 
come. A  borrower  is  a  seller  of  a  note  of  which  the  lender 
is  the  buyer.  A  bondholder  is  regarded  indifferently  as  a 
lender  and  as  a  buyer  of  property.  The  concept  of  a  loan 
may  therefore  now  be  dispensed  with  by  being  merged  in  that 
of  sale.  By  selling  some  property  rights  and  buying  others 
it  is  possible  to  transform  one's  income-stream  at  will, 
whether  in  time-shape,  composition,  or  probability.  Thus, 
if  a  man  buys  an  orchard,  he  is  providing  himself  with  future 
income  in  the  use  of  apples ;  if,  instead,  he  buys  apples,  he 
is  providing  himself  with  similar  but  more  immediate 
income.  If  he  buys  securities,  he  is  providing  himself 
with  future  money,  convertible  when  received  into  true 
income.  If  his  security  is  a  share  in  a  mine,  his  income- 
stream  is  less  lasting,  though  it  should  be  larger,  than  if 
the  security  is  stock  in  a  railway.     Purchasing  the  right  to 


126  THE  RATE  OF  INTEREST  [Chap.  VII 

remote  enjoyable  income  is  called  investing;  to  immediate 
enjoyable  income,  spending.  These,  however,  are  purely  rel- 
ative concepts,  for  "remote"  and  "immediate"  are  relative 
terms.  Buying  a  winter  overcoat  or  a  carpet  may  be  called 
investing,  and  on  the  other  hand,  buying  a  factory  or  a  ship 
may  be  called  spending.  And  yet  the  antithesis  between 
"spending"  money  and  "investing"  is  important;  it  is 
the  antithesis  between  immediate  and  remote  income.  The 
adjustment  between  the  two  determines  the  time-shape  of 
one's  income-stream.  Spending  increases  immediate  in- 
come but  robs  the  future,  whereas  investing  provides  for 
the  future  to  the  detriment  of  the  present. 

Popular  usage  has  devised  many  other  terms  and  phrases 
in  this  field,  most  of  which,  like  "spending"  and  "in- 
vesting," while  containing  meaning  of  importance,  include 
also  the  alloy  of  misconception.  Thus,  the  phrase  "  capital 
seeking  investment"  means  that  capitalists  have  property 
for  which  they  desire,  by  exchange,  to  substitute  other 
property,  the  income  from  which  is  more  remote.  It  does 
not  mean  that  the  inanimate  capital  has  of  itself  any  power 
to  "seek  investment";  it  does  not  mean  that  there  is  any 
hard  and  fast  line  between  invested  and  uninvested  capital. 
Again,  the  phrase  "saving  capital  out  of  income"  means 
"not  spending,"  — reserving  money  which  would  otherwise 
be  spent  for  immediate  enjoyable  income  in  order  to  ex- 
change it  for  remoter  income ;  it  does  not  mean  the  creation 
of  new  capital,  though  it  may  lead  to  it.  Many  needless  con- 
troversies have  centered  about  the  phenomenon  of  "sav- 
ing," chiefly  because  neither  "saving"  nor  "income"  was 
clearly  defined.^ 

From  what  has  been  said  it  is  clear  that  by  buying  and 
selling  property  an  individual  may  change  the  conformation 


'  Thus,  by  "  saving,"  some  writers  understand  that  capital  neces- 
sarily increases,  and   hence    the  income-stream  is  made  to  ascend; 
others,  like  Carver  {loc.  cit.  p.  232),  apply  the  term  broadly  enough  to 
include  the  case  where  a  descending  income  is  simply  rendered  less 
descending.    The  latter  view  harmonizes  with  that  here  presented. 


Sec.  5]  FIRST  APPROXIMATION ;  127 

of  his  income-stream  precisely  as  though  he  were  specifically 
lending  or  borrowing.  Thus,  if  a  man's  original  income- 
stream  is  $1000  this  year  and  $1500  next  year,  and  if, 
selling  this  income-stream,  he  buys  with  the  proceeds 
another  yielding  $1100  this  year  and  $1395  next  year,  he 
has  not,  nominally,  borrowed  $100  and  repaid  $105,  but 
he  has  done  what  amounts  to  the  same  thing,  —  increased 
his  income-stream  of  this  year  by  $100  and  decreased  that 
of  next  year  by  $105,  the  $100  being  the  modification  pro- 
duced in  his  income  for  the  first  year  by  selling  his  original 
income-stream  and  substituting  the  final  one,  and  $105 
being  the  reverse  modification  in  next  year's  income 
produced  by  the  same  operations.  The  very  same  dia- 
grams which  were  used  before  may  be  taken  to  represent 
these  operations.  A  man  sells  the  income-stream  ABCD 
(Fig.  6)  and  with  the  proceeds  buys  the  stream  EBD. 
The  X'  and  X"  are,  as  before,  $100  and  $105,  but  now 
appear  explicitly  as  differences  in  the  value  of  two  income- 
streams  instead  of  direct  loans  and  returns. 

§  5 

In  passing  we  may  note  that  interest-taking  cannot  be 
prevented  by  prohibiting  loan  contracts.  To  forbid  the 
particular  form  of  sale  called  a  loan  contract  would 
leave  possible  other  forms  of  sale,  and,  as  was  shown 
in  The  Nature  of  Capital  and  Income,  the  valuation  of 
every  property-right  involves  interest.  If  the  prohibition 
left  individuals  free  to  deal  in  bonds,  it  is  clear  that  they 
would  be  still  borrowing  and  lending,  but  under  the  name 
of  "sale" ;  and  if  " bonds"  were  tabooed,  they  could  change 
the  name  to  "preferred  stock."  It  can  scarcely  be  sup- 
posed that  any  prohibition  of  interest-taking  would  extend 
to  all  buying  and  selling ;  but  as  long  as  buying  and  selling 
of  any  kind  were  permitted,  the  virtual  effect  of  lending  and 
borrowing  would  be  retained.  Tlie  possessor  of  a  forest 
of  young  trees,  not  being  able  to  mortgage  their  future 


128  THE  RATE  OF  INTEREST  [Chap.  VII 

return,  and  being  in  need  of  an  income-stream  of  a  less 
deferred  type  than  that  receivable  from  the  forest  itseK, 
would  simply  sell  his  forest  and  with  the  proceeds  buy,  say, 
a  farm,  with  a  uniform  flow  of  income,  or  a  mine  with  a 
decreasing  one.  On  the  other  hand,  the  possessor  of  a 
capital  which  is  depreciating,  that  is,  which  represents  an 
income-stream  great  now  but  steadily  declining,  and  who 
is  anxious  to  ''save"  instead  of  "spend,"  would  sell  his 
depreciating  wealth  and  invest  the  proceeds  in  such  instru- 
ments as  the  forest  already  mentioned. 

It  was  in  such  a  way,  as  for  instance  by  "rent  pm'chase," 
that  the  medieval  prohibitions  of  usiu-y  were  rendered 
nugatory.  Practically,  at  the  worst,  the  effect  of  restrictive 
laws  is  simply  to  hamper  and  make  difficult  the  finer  ad- 
justments of  the  income-stream,  compelling  would-be  bor- 
rowers to  sell  wealth  yielding  distant  returns  instead  of 
mortgaging  it,  and  would-be  lenders  to  buy  the  same, 
instead  of  lending  to  the  present  owners.  It  is  conceivable 
that  "explicit"  interest  might  disappear  under  such  restric- 
tions, but  "implicit"  interest  would  remain.  The  young 
forest  sold  for  $10,000  would  bear  this  price,  as  now,  because 
it  is  the  discounted  value  of  the  estimated  future  income; 
and  the  price  of  the  farm  bought  for  $10,000  would  be  de- 
termined in  like  manner.  The  rate  of  discount  in  the  two 
cases  must  be  the  same,  because,  by  buying  and  selling, 
the  various  parties  in  the  community  adjust  their  rates 
of  preference  to  a  common  level,  — an  implicit  rate  of  in- 
terest thus  lurking  in  every  contract,  though  never  specifi- 
cally appearing  therein.  Interest  is  too  omnipresent  a 
phenomenon  to  be  eradicated  by  attacking  any  particular 
form ;  nor  would  any  one  undertake  it  who  perceived  the 
substance  as  well  as  the  form.^  In  substance,  the  rate  of 
interest  represents  the  terms  on  which  the  earlier  and  later 
elements  of  income- streams  are  exchangeable. 


'Cf.  Fetter,  Principles  of  Economics,  New  York  (Century),  1904, 
pp.  134,  135. 


Sec.  6]  FIRST  APPROXIMATION  129 


§   6 


The  fact  that,  through  the  loan  market,  the  marginal 
rate  of  time-preference  for  each  individual  is  made  equal 
to  the  rate  of  interest,  may  be  stated  in  another  way, 
namely,  that  the  total  present  desirability  or  utility  of  the 
individual  income-stream  is  made  a  maximum.  For,  con- 
sider again  the  individual  who  modifies  his  original  fixed 
income-stream  by  borrowing  until  his  rate  of  preference  is 
brought  into  unison  with  the  rate  of  interest.  His  rate  of 
preference  was  at  first  10  per  cent. ;  that  is,  in  order  to 
secure  an  addition  of  $100  to  his  present  income,  he  was 
willing  to  sacrifice  $110  of  next  year's  income.  But  he 
only  needed  to  sacrifice  $105 ;  that  is,  he  was  enabled  to  get 
his  loan  for  less  than  he  would  have  been  willing  to  pay. 
He  was  therefore  a  gainer  to  the  extent  of  the  present  de- 
sirability of  $5  of  next  year's  income.  The  second  $100 
borrowed  was  equivalent,  in  his  present  estimation,  to 
$108  of  next  year's  income,  and  the  same  reasoning 
shows  that,  as  he  pays  only  $105,  he  saves  $3 ;  that  is,  he 
adds  the  present  desirability  of  $3  due  next  year  to  the 
present "  total  desirabihty "  or  "  total  utility"  of  his  income- 
stream.  In  like  manner,  each  successive  increment  of  loans 
adds  to  his  present  total  desirability,  so  long  as  he  is 
willing  to  pay  more  than  $105  of  next  year's  income  for 
$100  of  this  year's  income.  But,  as  he  proceeds,  his  gains 
and  his  eagerness  diminish  until  they  cease  altogether. 
At,  let  us  say,  the  fifth  instalment  of  $100,  he  finds  himself 
barely  willing  to  pay  $105;  his  present  total  desirability 
is  then  a  maximum,  and  any  further  loan  would  decrease 
it.  A  sixth  $100,  for  instance,  is  worth  in  his  estimation 
less  than  $105,  say  $104,  and  as,  in  the  loan  market,  he 
would  have  to  sacrifice  $105  next  year  to  secure  it,  the  con- 
tracting of  such  a  loan  would  mean  a  loss  of  desirability 
to  the  extent  of  $1  due  in  one  year.  Thus,  by  borrowing  up 
to  the  point  where  the  rate  of  preference  for  present  over 


130  THE  RATE  OF  INTEREST  [Chap.  VII 

future  income  is  equal  to  the  rate  of  interest,  the  individual 
secures  the  greatest  "total  desirability." 

Similar  reasoning,  applied  to  the  individual  on  the  other 
side  of  the  market,  whose  rate  of  preference  is  initially 
less  than  the  market  rate  of  interest,  will  show  that  he  also 
will  maximize  his  present  total  desirability  by  lending  up 
to  the  point  where  his  rate  of  preference  corresponds  to  the 
rate  of  interest.  At  the  beginning,  $100  this  year  has  to 
him  the  same  present  desirability  as  .$102  due  one  year 
hence,  whereas  in  the  market  he  may  secure  $105.  It  is 
then  clear  that  by  lending  $100  he  gains  the  present  desira- 
bility of  $3  due  one  year  hence.  By  lending  each  successive 
$100  he  will  add  something  to  his  total  present  desirability, 
until  his  rate  of  preference  for  present  over  future  income 
is  raised  to  a  level  equal  to  that  of  the  rate  of  interest. 
Beyond  that  point  he  would  lose  by  further  lending;  but 
at  that  point  he  will  stop,  and  his  present  total  desirability 
will  therefore  be  a  maximum. 


§  7 


We  are  now  in  a  position  to  give  a  preliminary  answer 
to  the  question.  What  determines  the  rate  of  interest? 
Thus  far  we  have  regarded  the  individual  only,  and  have 
seen  that  he  conforms  his  rate  of  preference  to  the  rate  of 
interest.  For  him  the  rate  of  interest  is  a  relatively  fixed 
fact,  since  his  own  time-preference  and  resulting  action 
can  affect  it  only  infinitesimally.  His  rate  of  preference 
is  the  variable.  In  short,  for  him  individually  the  rate  of 
interest  is  cause,  and  the  rate  of  preference,  effect.  For 
society  as  a  whole,  however,  the  order  of  cause  and  effect 
is  reversed.  This  change  is  like  the  corresponding  inversion 
of  cause  and  effect  in  the  theory  of  prices.  Each  individual 
regards  the  market  price,  say,  of  sugar,  as  fixed,  and  adjusts 
his  marginal  utility  to  it;  whereas,  for  the  entire  group 
forming  the  market,  we  know  that  the  price  of  sugar  is  due 


Sec.  7]  FIRST  APPROXIMATION  131 

to  its  marginal  utility  to  the  consumer/  In  the  same  way, 
while  for  the  individual  the  rate  of  interest  determines  the 
rate  of  preference,  for  society  the  rates  of  preference  of 
the  individuals  determine  the  rate  of  interest.  The  rate 
of  interest  is  simply  the  rate  of  preference,  upon  which  the 
whole  community  may  concur  in  order  that  the  market 
of  loans  may  be  exactly  cleared. 

To  put  the  matter  in  figures :  if  the  rate  of  interest  is 
set  very  high,  say  20  per  cent.,  there  will  be  relatively 
few  borrowers  and  many  would-be  lenders,  so  that  the 
total  extent  to  which  would-be  lenders  are  willing  to 
reduce  their  income-streams  for  the  present  year  for  the 
sake  of  a  much  larger  future  income  will  be,  say,  100 
million  dollars ;  whereas,  those  who  are  willing  to  add  to 
their  present  income  at  the  high  price  of  20  per  cent, 
interest  will  borrow  only,  say,  one  million.  Under  such 
conditions  the  demand  for  loans  is  far  short  of  the  supply 
and  the  rate  of  interest  will  therefore  go  down.  At  an 
interest  rate  of  10  per  cent,  the  present  year's  income 
offered  as  loans  may  be  50  millions,  and  the  amount  which 
would  be  taken  at  that  rate  only  20  millions.  There  is 
still  an  excess  of  supply  over  demand,  and  interest  must 
needs  fall  further.  At  5  per  cent,  we  may  suppose  the 
market  cleared,  borrowers  and  lenders  being  willing  to  take 
or  give  respectively  30  millions.  In  like  manner  it  can 
be  shown  that  the  rate  would  not  fall  below  this,  as  in 
that  case  it  would  result  in  an  excess  of  demand  over 
supply  and  cause  the  rate  to  rise  again. 

Thus,  the  rate  of  interest  is  the  common  market  rate  of 
preference  for  present  over  future  income,  as  determined  by 
the  supply  and  demand  of  present  and  future  income.  Those 
who,  having  a  high  rate  of  preference,  strive  to  acquire 
more  present  income  at  the  cost  of  future  income,  tend  to 
raise  the  rate  of  interest.     These  are  the  borrowers,  the 

*  See  the  author's  "Mathematical  Investigations  in  the  Theory 
of  Value  and  Prices,"  Transactions  of  Connecticut  Academy,  New 
Haven,  1892,  p.  28. 


132  THE   RATE  OF  INTEREST  [Chap.  VII 

spenders,  the  sellers  of  property  yielding  remote  income, 
such  as  bonds  and  stocks.  On  the  other  hand,  those  who, 
having  a  low  rate  of  preference,  strive  to  acquire  more 
future  income  at  the  cost  of  present  income,  tend  to  lower 
the  rate  of  interest.  These  are  the  lenders,  the  savers, 
the  investors. 

The  mechanism  just  described  will  not  only  result  in  a 
rate  which  will  clear  the  market  for  loans  connecting  the 
present  with  next  year,  but,  applied  to  exchanges  between 
the  present  and  the  remoter  future,  it  will  make  similar 
adjustments.  While  some  individuals  may  wish  to  ex- 
change this  year's  income  for  next  year's,  others  wish  to 
exchange  this  year's  income  for  that  of  the  year  after  next, 
or  for  a  portion  of  several  years'  future  incomes.  The 
rates  of  interest  for  these  various  periods  are  so  adjusted 
as  to  clear  the  market  for  all  the  periods  of  time  for  which 
contracts  are  made. 

If  we  retain  our  original  assumption  that  every  man  is 
initially  endowed  with  a  fixed  and  certain  income-stream 
which,  by  borrowing  and  lending,  can  be  freely  bought  and 
sold  and  thereby  redistributed  in  time,  the  foregoing  dis- 
cussion gives  us  a  complete  theory  of  the  causes  which 
determine  the  rate  of  interest,  or  rather,  the  rates  of  interest 
for  various  time-periods.  These  rates  of  interest  would, 
under  these  circumstances,  be  fully  determined  by  the  fol- 
lowing four  conditions,  to  which  all  the  magnitudes  in  the 
problem  of  interest  must  conform: — 

(1)  The  rate  of  time-preference  of  each  individual  for 
present  income,  as  compared  with  remoter  income,  depends 
upon  the  character  of  his  income-stream,  as  finally  modified 
and  determined  by  the  very  act  of  borrowing  or  lending, 
buying  or  selling. 

(2)  Through  the  variations  in  the  income-stream  pro- 
duced by  loans  or  sales,  the  rates  of  preference  for  all 
individuals  in  the  market  are  brought  into  equality  with 
each  other  and  with  the  market  rate  of  interest. 

This  condition  is  equivalent  to  another;   namely,  that 


Sec.  7]  FIRST  APPROXIMATION  133 

each  individual  exchanges  present  against  future  income, 
or  vice  versa,  at  the  market  rate  of  interest  up  to  the 
point  of  maximum  desirability. 

(3)  The  market  rate  of  interest  will  be  such  as  will  just 
clear  the  market ;  namely,  will  make  the  loans  and  borrow- 
ings cancel  each  other  for  each  period  of  time. 

(4)  All  loans  are  repaid  with  interest ;  that  is,  the  present 
value  of  the  payments,  reckoned  at  the  time  of  contract, 
equals  the  present  value  of  the  repayments.  More  gener- 
ally, the  modifications  or  departures  from  a  person's  origi- 
nal income-stream  effected  by  buying  and  selling  are  such 
that  the  algebraic  sum  of  their  present  values  is  zero. 

These  four  conditions  not  only  determine  the  rate  of 
interest,  but  determine  also  all  the  other  variable  elements 
which  enter  into  the  problem ;  namely,  the  individual  rates 
of  preference  (equal  to  the  rate  of  interest)  and  the 
amounts  which  are  borrowed  and  lent. 

The  formulation  of  these  four  determining  conditions 
constitutes  our  first  approximation  to  the  theory  of  interest. 
The  sufficiency  of  the  four  conditions  and  their  coordination 
may  be  made  clear  by  means  of  the  mathematical  statement 
contained  in  the  Appendix  to  this  chapter. 


PART  III.   Second  and  Third  Approximations 

Chapter  VIII.     Second  Approximation  to  the  theory  of 

INTEREST  (assuming  INCOME  FLEXIBLE) 

Chapter     IX.     Classes  of  Options 
Chapter      X.     Invention 

Chapter     XI.     Third   Approximation   to  the  theory  of 

interest  (assuming  income  uncertain) 


=         HOSS.  MOREWEDGE 

-  P.  O.  Box  2734 

—  Hollywood   28,   California 


CHAPTER  VIII 

SECOND    APPROXIMATION     TO    THE    THEORY     OF     INTEREST 
(assuming    INCOME    FLEXIBLE) 

§1 

Hitherto  we  have  assumed  that  the  income-stream 
flowing  from  any  given  article  of  capital  is  both  fixed  and 
certain.  We  now  abandon  the  first  part  of  this  hypothesis. 
Still  assuming  that  all  income-streams  are  certain,  that  is, 
can  be  definitely  foreseen,  we  now  introduce  the  hypothesis 
that  they  are  not  fixed,  but  flexible ;  that  is,  that  the  owner 
of  any  capital-wealth  or  capital-property  is  not  restricted 
to  a  single  use  to  which  he  may  put  it,  but  has  open  to  his 
choice  several  different  uses,  each  of  which  constitutes  a 
separate  optional  income-stream. 

For  instance,  the  owner  of  land  may  use  it  in  more 
than  one  way.  He  may  use  it  to  grow  crops,  graze  animals, 
plant  forests,  extract  minerals,  support  buildings,  or  for 
other  purposes.  Again,  the  owner  of  a  building  may  use 
it  for  office  purposes,  for  apartments,  or  for  stores.  Most 
raw  materials  can  be  used  for  any  one  of  a  number  of  pur- 
poses. Iron  may  be  wrought  into  steel  rails  or  into  ma- 
chinery, implements,  tools,  armor  for  ships,  or  girders  for 
buildings.  A  derrick  may  be  used  for  quarrying  stone, 
building  a  house,  or  unloading  a  boat.  A  ship  may  be  used 
to  carry  any  sort  of  cargo,  and  over  any  one  of  numerous 
different  routes.  Hammers,  saws,  nails,  and  other  tools 
may  be  used  in  almost  numberless  ways. 

Perhaps  the  most  adaptable  of  all  instruments  of  wealth 
is  man  himself.    He  may  be  simply  a  passive  enjoyer  or 

137 


138  THE   RATE   OF   INTEREST  [Chap.  VIII 

"transformer"  ^  of  the  services  of  other  wealth,  and  as  such 
derive  his  satisfactions  in  sensual,  esthetic,  intellectual,  or 
spiritual  ways ;  or,  he  may  also  be  an  active  producer,  and 
as  such  perform  physical  or  mental  work.  If  his  work  is 
physical,  it  may  consist  in  anything  from  wielding  a  pick 
and  shovel  to  the  deft  manipulation  of  the  instruments 
employed  in  the  jeweler's  art.  If  his  work  is  mental,  he 
may  be  a  bookkeeper,  clerk,  superintendent,  director,  law- 
yer, physician,  editor,  teacher,  or  scientist. 

In  consequence  of  such  a  range  of  choice,  the  same  set  of 
productive  instruments  may  result  in  very  different  income- 
streams.  Tlieir  energies  may  be  directed  at  will  to  pro- 
duce cheap  frame  houses  or  durable  stone  ones;  to  equip 
a  city  with  horse  cars,  trolleys,  or  underground  rapid 
transit;  to  secure  an  income-stream  which  shall  consist 
largely  of  the  pleasures  of  the  table,  or  of  the  amusements  of 
the  theater,  or  of  the  gratification  of  social  vanities,  —  in 
short,  to  select  one  particular  income-stream  out  of  a 
thousand  possible  income-streams  differing  in  size,  compo- 
sition, and  time-shape,  as  well  as  in  probability,  though  in 
this  chapter  the  element  of  uncertainty  is  supposed  absent. 

Owing  to  this  great  range  of  choice,  the  owner  of  capital 
may  modify  the  income-stream  he  derives  from  it,  not 
simply  by  the  devices  of  borrowing  and  lending  or  of  sell- 
ing and  buying,  but  also  by  changing  the  use  or  employ- 
ment to  which  his  capital  is  put.  It  should  be  noted, 
however,  that  this  third  method  of  modifying  an  income- 
stream  really  includes  the  other  two.  Just  as  buying 
and  selling  virtually  include  borrowing  and  lending,  so  the 
change  from  one  use  of  capital  to  another  may  be  said  to 
include  buying  and  selling,  and  therefore  also  to  include 
borrowing  and  lending.  This  is  evident  if  we  consider  that 
one  method  of  employing  capital  is  to  sell  it.  In  fact,  a 
merchant  regards  himself  as  "using"  his  stock  in  the  ex- 
clusive sense  of  selling  it. 

This  method  of  modifying  the  income-stream  is  therefore 

*  See  The  Nature  of  Capital  and  Income,  Chap.  X. 


Sec.  2]  SECOND  APPROXIMATION  139 

a  general  one.  But,  while  it  includes  the  other  methods, 
it  includes  much  else  so  different  from  the  methods  of 
borrowing  and  lending  or  buying  and  selling  that  we  shall 
need  to  distinguish  the  new  method  from  the  old.  There 
are  two  principal  reasons  for  keeping  the  new  method 
separate.  First,  the  former  and  narrower  methods  of 
modifying  income-streams  cannot  be  applied  to  society  as 
a  whole.  Society  as  a  whole  cannot  borrow  and  lend,  nor 
buy  and  sell ;  and  yet  it  can  radically  change  the  character 
of  its  income-stream  by  changing  the  employment  of  its 
capital.  Secondly,  when  borrowing  and  lending  or  ordi- 
nary buying  and  selling  are  employed  to  modify  an 
income-stream,  the  present  values  of  the  original  in- 
come-stream and  of  the  modified  income-stream  are  the 
same.  But  when  an  income-stream  is  modified  by  a 
change  in  the  use  of  the  capital  yielding  it,  its  present 
value  may  not  remain  the  same. 


§  2 


The  choice  among  the  various  optional  income-streams 
will  fall  on  the  one  which  has  the  maximum  desirability.  As 
among  income-streams  of  different  sizes  but  alike  in  com- 
position and  time-shape,  the  most  desirable  will  of  course 
be  the  largest ;  as  among  income-streams  of  different  com- 
position but  alike  in  other  respects,  the  most  desirable  will  be 
that  in  which  the  marginal  desirabilities  of  the  different  con- 
stituents are  proportional  to  their  several  prices,  in  accordance 
with  a  fundamental  principle  in  the  theory  of  prices ;  finally, 
as  among  income-streams  differing  in  time-shape,  the  most 
desirable  is  found  in  accordance  with  the  principles  which 
govern  the  rate  of  interest.  It  is  therefore  with  the  differ- 
ences in  time-shape  that  we  are  here  chiefly  concerned. 

To  illustrate  these  differences,  let  us  suppose  an  individual 
possessed  of  a  piece  of  land  almost  equally  good  for  lumber- 
ing, farming,  or  mining.     He  thus  has  the  option  of  using 


140 


THE   RATE  OF  INTEREST 


[Chap.  VIII 


it  in  any  one  of  three  different  ways:  (1)  in  farming, 
which,  let  us  say,  will  give  him  a  regular  and  indefinite 
succession  of  crops  with  an  income-stream  of  the  type  A  in 
Figure  15 ;  (2)  for  forest  purposes,  with  very  slight  returns 
for  the  first  few  decades,  and  larger  returns  in  the  futm'e, 
as  indicated  by  the  curve  B;  (3)  for  mining  purposes,  in 
which  case  we  shall  suppose  that,  as  the  mining  plant  is 
already  set  up  and  the  richest  ore  lies  close  to  the  surface, 
the  income  is  greatest  for  the  early  years  and  thereafter 
gradually  decreases  until  the  mine  is  exhausted.  This  is 
shown  by  curve  C.  Wliat  are  the  principles  upon  which 
the  owner  of  the  land  chooses  among  these  three  income- 
streams  ? 


B 


Fig.  15. 


We  shall  suppose,  as  heretofore,  that  there  is  a  uniform 
rate  of  interest,  and  that  any  individual  is  free  either  to 
borrow  or  lend  at  that  rate  to  any  required  amount. 
Under  this  hypothesis  the  choice  among  the  options  will 
simply  depend  on  the  one  which  gives  the  maximum 
present  value,  reckoned  at  the  market  rate  of  interest. 
Thus,  if  the  use  of  the  land  for  forestry  purposes  yields  the 
following  sums :  zero  for  the  first  two  years,  $300  for  the 
thu-d,  $400  for  the  fourth,  $500  for  the  fifth,  and  $500 
thereafter  forever,  —  then  the  value  of  the  land,  if  the  rate 
of  interest  is  5  per  cent.,  will  be  $8820.  If  the  land  is  used 
for  mining  purposes,  it  will  yield  an  income-stream  of 
quite  a  different  character,  let  us  say,  as  follows :   $2000 


Sec.  3]  SECOND  APPROXIMATION  141 

the  first  year,  $1800  the  second,  $1600  the  third,  and  so 
on  diminishing  annually  by  $200  to  the  point  of  exliaustion. 
The  present  value  of  these  sums  is  $9110.  If,  finally,  the 
land  is  used  for  farming  purposes  and  yields  a  net  income 
of  $450  a  year  perpetually,  the  present  value  will  be  $9000. 
Under  these  conditions  the  choice  will  evidently  fall  on  the 
mining  use,  because,  for  mining  purposes,  the  land  is  worth 
$9110,  which  is  greater  than  $8820,  its  value  for  forestry 
purposes,  and  than  $9000,  its  value  for  farming  purposes. 

The  particular  income-stream  selected  will  leave  its  im- 
press on  the  time-shape  of  the  total  income-stream  of  the 
individual  who  owns  it.  For,  as  was  seen  in  The  Nature 
of  Capital  and  Income,^  the  total  final  income-stream  of 
any  individual  is  simply  the  sum  of  the  incomes  flowing 
from  all  the  articles  of  property  belonging  to  him.  Hence, 
if  one  selects  the  mining  use  for  his  land,  whereby  the 
income-stream  gradually  decreases,  its  tendency  will  be 
to  produce  a  similar  decrease  in  the  total  income-stream 
possessed  by  the  individual.  This  tendency  may,  of  course, 
be  counteracted  by  some  opposing  tendency,  but  will  have 
full  sway  if  the  income  from  all  other  capital  than  the 
land  remains  the  same  in  value  and  time-shape. 

It  is  true  that  the  income  from  the  mine  is  not  final 
enjoyable  income,  but  consists  of  "interactions."  But 
these  interactions  are  readily  transformed,  through  a  chain 
of  credits  and  debits,  into  final  enjoyable  income.  The 
ore  of  the  mine  is  exchanged  for  money,  and  the  money 
spent  for  enjoyable  services  or  for  commodities  which  soon 
yield  enjoyable  services,  so  that  the  "enjoyable"  income 
follows  closely  behind  the  "intermediate"  income  from  the 
mine,  and  almost  exactly  copies  it  in  time-shape.^ 

§  3 

Yet  the  possessor  of  the  mine  is  not  compelled  to  copy  in 
his  final  enjoyable  income  the  mine's  fluctuations  of  natural 

»  Chaps.  VII-X,  XVII. 

*  See  The  Nature  of  Capital  and  Income,  Chaps.  VIII,  IX,  XVII. 


142  THE  RATE  OF  INTEREST  [Chap.  VIII 

income.  He  may,  for  instance,  prefer  as  his  model  an  even 
flow  of  income  such  as  he  could  get  from  the  farm-use  of 
his  land.  He  will  not,  however,  on  that  account  choose 
this  farm-use  in  preference  to  the  mining-use ;  for  the  min- 
ing-use has  the  larger  present  value,  and  the  undesirable 
time-shape  of  its  income-stream  can  be  remedied  by  the 
methods  explained  in  the  previous  chapter,  —  by  lending 
at  interest  the  proceeds  of  its  earlier  output  and  postponing 
enjoyable  income  to  later  years;  or,  more  generally,  by 
bmjing  with  the  early  proceeds  such  property  as  will 
yield  returns  at  such  future  times  as  are  most  desired,  — 
in  short,  by  "investing"  instead  of  "spending."^  The 
difference  is  merely  that  if  he  "spends"  the  yield  from  his 
mine,  he  is  exchanging  it  for  property  from  which  enjoy- 
able income  comes  promptly,  whereas  if  he  "invests,"  he 
is  exchanging  it  for  property  from  which  enjoyable  income 
comes  more  tardily.  If  he  "spends"  the  mine's  income 
as  fast  as  he  receives  it,  for  food,  clothing,  shelter,  travel, 
amusements,  his  "enjoyable"  income  simply  shadows  the 
"  intermediate"  income  from  the  mine;  but  if  he  "invests" 
the  mine's  income  in  more  durable  forms,  such  as  furniture, 
or  still  better,  dwellings,  or  stocks  and  bonds,  his  enjoy- 
able income  lags  further  behind  the  income  from  the  mine 
on  which  it  depends,  and  by  proper  manipulation  can  be 
distributed  in  time  in  any  desired  manner,  —  for  instance, 
evenly,  as  above  supposed. 

Since  the  mining-use  has  the  higher  present  value,  there 
is  an  advantage  in  selecting  it  rather  than  the  farm-use 
which  has  the  more  desirable  time-shape;  for  after  the 
minmg  income  is  converted  into  the  same  time-shape  as 
the  farming  income,  it  will  be  greater  in  magnitude,  in  the 
ratio  of  their  present  values,^  9110 :  9000. 

>  See  Chap.  VII,  §  4. 

^  This  is  evident  from  the  principles  explained  in  The  Nature  of  Cap- 
ital and  Income,  Chap.  XIII;  for  the  mining  income,  after  conversion 
by  investment  at  5  per  cent.,  will  still  have  the  same  present  value, 
$9110,  and  the  even  income  of  which  this  is  present  value  is  at  5  per 
cent.,  $455.50,  instead  of  the  f450  which  the  farm-use  yields.    The 


Sec.  3] 


SECOND  APPROXIMATION 


143 


Again,  it  may  be  that  the  mine  owner  prefers,  not  a 
steady,  but  an  ascending  income-stream,  and  as  in  the  case 
just  considered,  he  may  secure  such  an  income  by  modify- 
ing the  income  by  means  of  properly  graduated  investments 
of  the  early  parts  of  the  mine's  income.  He  can  secure,  if 
he  likes,  exactly  the  same  time-shape  as  though  he  had 
chosen  the  forestry  use,  with  the  advantage  that  his  income 
will  be  larger.  Thus,  he  may  invest  all  of  his  first  two  years' 
income  of  $2000  and  $1800  respectively,  $1290  in  the  third 
year,  $987  in  the  fourth  year,  and  so  on,  reducing  his 
annual  investments  by  the  proper  gradations ;  and,  proceed- 
ing at  the  proper  time  to  "realize"  on  these  investments, 
he  may  obtain,  as  the  final  result  of  these  operations, 
an  income  of  precisely  the  same  time-shape  as  that  which 
he  would  have  obtained  from  the  forestry  use.  But  the 
size  of  the  income  will  be  larger  in  the  ratio  of  the  present 
values  of  the  mining  and  forestry  income-streams,  9110 : 
8820.    The  following  table  exliibits  these  operations :  — 


As  against 

Receives 
FROM  Mines 

From  which 

HE  Invests 

So  THAT 

HIS  Income 
is 

WHAT  THE 

Forest  Use 

would  have 

Yielded 

1st  year 

2000 

2000 

000 

000 

2d  year 

1800 

1800 

000 

000 

3d  year 

1600 

1290 

310 

300 

4th  year 

1400 

987 

413 

400 

5th  year 

1200 

684 

516 

500 

6th  year 

1000 

484 

516 

500 

7th  year 

800 

284 

516 

500 

8th  year 

600 

84 

516 

500 

9th  year 

400 

-116 

516 

500 

10th  year 

200 

-316 

516 

500 

mine  owner  needs  simply  to  invest  annually  the  excess  of  his  income 
above  .$455.50;  namely,  $1544.50  in  the  first  year,  $1344.50  in  the 
second  year,  etc.  When  the  ninth  year  is  reached  the  mvestment 
ceases,  for  the  mine  then  yields  only  $400.  This  is  then  eked  out 
by  $55.50  from  the  amounts  previously  invested,  and  the  same 
methods  are  pursued  thereafter. 


144  THE  RATE  OF  INTEREST  [Chap.  VIII 

Since  any  time-shape  may  be  transformed  into  any  other 
no  one  need  be  deterred  from  selecting  an  income  because 
of  its  time-shape,  but  may  choose  it  exclusively  on  the 
basis  of  maximum  present  value.  On  the  other  hand, 
were  it  not  for  the  possibility  of  modifying  the  time-shape 
of  his  income-stream  by  borrowing  and  lending  or  buying 
and  selling,  the  land  owner  would  not  feel  free  to  choose 
the  one  from  among  the  three  optional  employments  of 
his  land  which  possessed  the  highest  value,  but  might  be 
forced  to  take  one  of  the  others.  We  assume  in  this 
chapter  that,  after  the  most  valuable  option  has  been 
chosen,  it  is  possible  to  borrow  and  lend  or  to  buy  and 
sell  ad  libitum,.  It  will  then  happen  that  his  income  as 
finally  transformed  will  be  larger  than  it  could  have  been 


b" 


Fia.  16. 

if  he  had  chosen  some  other  use  which  afforded  that  same 
time-shape. 

To  illustrate  this  by  a  diagram,  let  AB  and  A^B'  in  Figure 
16  be  alternative  income-streams,  of  which  the  descending 
income-stream  AB  has  a  larger  present  value  than  the  as- 
cending income-stream  A'B'.  The  choice  will  then  fall  on 
AB,  even  though  the  individual  prefers  the  time-shape  of 


Sec.  4]  SECOND  APPROXIMATION  145 

the  other  income-stream  A'B\  He  will  then  lend  some  of 
the  early  receipts  from  the  income-stream  AB  and  receive 
back  some  of  the  later,  converting  his  income  AB  of  unde- 
sirable shape  into  the  income-stream  A"B"  which  has 
the  desired  shape.  Consequently  this  final  income  A"B'' 
combines  the  virtues  of  both  the  original  alternative  incomes 
AB  and  of  A'B' ;  it  possesses  the  superior  shape  of  A'B^ 
and  the  superior  present  worth  of  AB.  As  compared  with 
A'B'  it  has  the  same  shape  but  a  greater  size. 

We  see,  then,  that  the  capitalist  reaches  his  fuial  income 
through  the  cooperation  of  two  separate  kinds  of  choice  of 
incomes,  —  first,  the  choice  of  the  income-stream  which 
has  the  highest  present  value,  and  second,  the  choice  among 
different  possible  modifications  of  this  income-stream  by 
borrowing  and  lending  or  buying  and  selling.  These  two 
kinds  of  choice  are  distinguished  from  each  other  by  the 
fact  that  the  first  is  a  selection  among  optional  incomes  of 
different  market  values,  and  the  second  is  a  selection  among 
optional  incomes  of  the  same  market  value. 

§4 

Since  this  double  choice,  when  it  is  made,  results  in  a 
perfectly  definite  income-stream,  it  might  seem  that  the 
situation  does  not  materially  differ  from  the  case  of  a  rigid 
income-stream  discussed  in  the  preceding  chapter.  But 
the  two  cases  differ  materially;  for  in  the  present  case  of 
optional  income-streams,  the  particular  choice  depends 
upon  the  rate  of  interest.  A  change  in  that  rate  may  shift 
the  choice  of  maximum  present  value  to  some  other  alter- 
native. Thus,  in  the  example  cited,  if  the  rate  of  interest 
should  be  4|  per  cent,  instead  of  5  per  cent.,  the  order  of 
choice  would  be  changed.  The  value  of  the  land  for  fores- 
try use  would  be  $9920,  for  farming  use,  $10,000,  and  for 
mining  use,  $9280.  The  farming  use  would  now  be  the  best 
choice.  Again,  if  the  rate  of  interest  should  be  4  per  cent, 
instead  of  4^  per  cent.,  the  present  value  of  the  use  of  the 


146 


THE   RATE  OF   INTEREST 


[Chap.  VIII 


land  for  forest  purposes  would  be  $11,300,  for  farming 
purposes,  $11,250,  and  for  mining  purposes,  $9450.  In 
this  case  the  forestry  use  would  be  chosen.  We  see,  then, 
that  it  pays  best  to  employ  the  land  for  mining  if  the  rate 
of  interest  is  5  per  cent.,  for  farming  if  it  is  4^  per  cent., 
and  for  forestry  if  it  is  4  per  cent. 

The  various  options  open  to  the  owner  of  the  land  at 
different  rates  of  interest  are  summarized  in  the  following 
table :  — 


Optional  Uses 

Present  Value  at 

5% 

4r/o 

4% 

For  forestry 
For  farming 
For  mining  .... 

8,820 
9,000 
9,110 

9,920 

10,000 

9,280 

11,300 

11,250 

9,450 

Tlius  a  change  in  the  rate  of  interest  results  in  a  change 
in  the  choice  of  income-streams.  A  high  rate  of  interest 
will  encourage  investment  in  the  quickly  returning  in- 
comes, whereas  a  low  rate  of  interest  will  encourage  invest- 
ment in  incomes  which  yield  distant  returns.  As  the  busi- 
ness man  puts  it,  when  interest  is  high  he  can  less  afford 
to  wait  for  a  remote  return  because  he  will  "  lose  so  much 
interest." 

An  investor  will,  therefore,  make  very  different  choices 
according  as  interest  is  at  one  rate  or  another.  Conse- 
quently the  existence  of  optional  uses  of  capital  introduces 
a  new  variable  into  the  problem  of  interest-determination. 
To  the  individual,  the  rate  of  interest  will  determine  the 
choice  among  his  optional  income-streams ;  but  for  society, 
the  order  of  cause  and  effect  is  reversed,  —  the  rate  of  in- 
terest will  be  influenced  by  the  existence  of  the  options. 
To  trace  this  influence  is  the  purpose  of  the  present  chapter. 


Sec.  5]  SECOND  APPROXIMATION  147 


§  5 


At  first  sight  it  may  appear  that  we  are  reasoning  in  a 
circle:  the  rate  of  interest  depends  on  individual  rates  of 
preference;  the  rates  of  preference  depend  on  the  time- 
shapes  of  individual  income-streams;  and  the  choice  of 
these  time-shapes  of  income-streams  depend,  we  have  just 
seen,  on  the  rate  of  interest  itself. 

It  is  perfectly  true  that  the  rate  of  interest  depends 
on  a  series  of  factors  which  finally  depend  on  the  rate  of 
interest.  Yet  this  series  is  not  the  vicious  circle  it  seems, 
for  the  last  step  is  not  the  inverse  of  the  first. 

To  distinguish  between  a  true  and  a  seeming  example 
of  a  circular  dependence  we  may  contrast  the  following  two 
simple  problems:  We  wish  to  find  the  height  of  a  father 
who  is  known  to  be  three  times  as  tall  as  his  child.  To 
solve  this  we  need  to  know  something  about  the  height  of 
the  child.  If  we  are  told  that  the  child's  height  differs 
from  his  father's  by  twice  itself,  the  problem  is  circular 
and  insoluble,  for  the  last  step  is  reducible  to  the  first,  being 
merely  a  concealed  inversion  of  it.  The  problem  essen- 
tially states  that  the  father's  height  is  three  times  the 
child's  and  the  child's  one  third  of  the  father's, — an  ob- 
vious circle.  But  if  the  dependence  of  the  father's  height 
on  the  child's  were  essentially  different  from  that  of  the 
child's  on  its  father's,  there  would  be  no  circle.  Thus, 
suppose  as  before  that  the  father  is  three  times  as  tall  as 
the  child,  but  that  the  child's  height  differs  from  the 
father's  by  four  times  the  child's,  less  four  feet.  This 
sounds  as  circular  as  the  fu-st  problem, — the  father's 
height  is  expressed  in  terms  of  the  child's,  and  the  child's  in 
terms  of  the  father's ;  but  here  the  second  expression  is  not 
reducible  to  the  first.  The  heights  are  entirely  determinate, 
that  of  the  father  being  six  feet  and  that  of  the  child,  two. 
The  mere  fact  that  each  of  these  magnitudes  is  specified  in 
terms  of  the  other  does  not  constitute  a  vicious  circle. 


148  THE  RATE   OF   INTEREST  [Chap.  VIII 

The  same  is  true  in  our  present  problem.  Real  examples 
of  circular  reasoning  in  the  theory  of  interest  are  common 
enough,  and  many  of  them  have,  in  fact,  been  noted  in  earher 
chapters,  but  the  dependence  above  stated,  of  interest  on  the 
range  of  options  and  of  the  choice  among  those  options  on 
interest,  is  not  a  case  in  point.  The  logical  principle  holds 
true  that  any  problem  is  determinate  if  only  there  are  as 
many  determining  conditions  as  there  are  unknown  quan- 
tities; it  is  only  necessary  that  these  conditions  shall  be 
*' independent" ;  in  other  words,  that  no  one  shall  be 
derivable  from  the  others.  That  this  is  mathematically 
the  case  under  our  present  hypothesis  is  shown  fully  in 
the  Appendix  to  this  chapter.  For  our  present  purpose  we 
need  only  present  the  matter  to  the  reader's  imagination  by 
a  series  of  successive  approximations. 

To  find  out  the  rate  of  interest  on  which  the  market  will 
finally  settle,  let  us  try  successively  a  number  of  different 
rates.  First,  suppose  a  rate  of  5  per  cent.  This  rate  will 
determine  the  choice  of  income-streams  for  each  individual. 
The  landowner  formerly  supposed  will,  as  we  have  seen, 
choose  the  mining-use.  Every  other  individual  in  the 
market,  in  like  manner,  will  select  that  particular  use  for 
his  capital  which  will  give  him  the  maximum  present  worth. 
With  these  choices  made,  the  different  individuals  will  then 
enter  the  market  of  loans  or  sales,  desiring  to  modify  the 
time-shapes  of  their  income-streams  to  suit  their  particular 
desires.  The  amount  which  the  would-be  lenders  are  will- 
ing to  lend  at  5  per  cent,  out  of  this  year's  instalment  of 
their  chosen  income-stream  will  be  perfectly  definite,  and 
likewise  the  amount  which  the  would-be  borrowers  are 
willing  to  take.  This  we  saw  in  the  preceding  chapter.  In 
other  words,  the  demand  and  supply  of  loans  for  the  present 
year  for  the  given  rate  of  interest,  5  per  cent.,  will  be  definite 
quantities.  Should  it  happen  that  the  demand  for  loans 
is  less  than  the  supply,  it  follows  that  5  per  cent,  cannot 
be  the  correct  solution  of  the  rate  of  interest,  for  it  is  too 
high  to  clear  the  market. 


Sec.  6]  SECOND  APPROXIMATION  149 

In  that  case,  let  us  suppose  a  rate  of  4  per  cent.  Follow- 
ing the  same  reasoning  as  before,  we  find  that  the  landowner 
will  now  select  the  forestry  use  for  his  land.  Other  capital- 
ists will  select  likewise  their  definite  income-streams,  and 
on  the  basis  of  these  income-streams  there  will  be  the  con- 
sequent desire  to  borrow  and  lend.  Should  it  then  happen 
that  the  demand  and  supply  of  loans,  on  the  basis  of  4 
per  cent.,  are  not  equal,  but  that  this  time  the  demand  ex- 
ceeds the  supply,  it  is  a  proof  that  not  4  per  cent,  is  the  true 
solution,  but  some  higher  rate.  By  again  changing  our 
trial  rate  back  toward  5  per  cent,  we  may  evidently  reach 
some  intermediate  point,  let  us  say  4^  per  cent.,  at  which 
rate  not  only  will  all  individuals  choose  definite  income- 
streams,  but  also,  at  the  same  time,  the  demand  and  supply 
of  loans  engendered  by  these  income-streams  will  exactly 
clear  the  market. 

The  introduction,  therefore,  of  flexibility  into  our  in- 
come-stream still  leaves  the  problem  of  interest  entirely 
determinate.  Though  the  income-streams  are  now  a  mat- 
ter of  choice,  there  is  one  definite  choice  corresponding 
to  each  rate  of  interest.  The  particular  rate  of  interest 
which  will  solve  the  problem  is  that  which  will  both  deter- 
mine the  choice  among  income-streams  differing  in  present 
value,  and  also  bring  it  about  that  individual  departures 
from  such  income-streams  shall  mutually  cancel  each  other, 
—  in  other  words,  that  the  markets  for  loans  and  sales 
shall  be  cleared. 

§  6 

For  the  determination  of  the  rate  of  interest  we  have 
therefore  to  modify  the  various  conditions  as  given  in  the 
previous  chapter.  The  modifications  which  are  introduced 
are,  (1)  that  in  place  of  the  single  fixed  income-stream 
formerly  assumed,  there  now  exists  a  given  range  of  choice 
between  different  income-streams;  and  (2)  that  whereas 
formerly  the  individual  had  no  choice  of  income-streams, 


150  THE  RATE  OF  INTEREST  [Chap.  VIII 

he  now  chooses  out  of  those  available  the  one  which  pos- 
sesses the  maximum  present  value.  We  therefore  have  six 
conditions  determining  the  rate   of   interest,  as   follows: 

(1)  There  exists  for  each  individual  a  given  series  of 
possible  income-streams    among   which   he   may  choose; 

(2)  Each  individual's  preference  rate  depends  upon  his 
income-stream,  —  its  size,  shape,  composition,  and  proba- 
bility; (3)  The  rates  of  preference  of  different  individuals 
must  be  equal  to  each  other  and  to  the  rate  of  interest  in 
the  market;  (4)  Out  of  all  available  income-streams,  that 
one  is  selected  which  has  the  maximum  present  value  for 
the  rate  of  interest  finally  determined ;  (5)  The  rate  of  in- 
terest must  be  such  as  will  equalize  supply  and  demand,  or 
exactly  clear  the  market ;  (6)  The  additions  to  and  deduc- 
tions from  each  income-stream,  brought  about  by  borrowing 
and  lending  or  buying  and  selling,  must  be  such  that  their 
net  present  value  is  zero. 

As  to  the  first  condition,  viz.,  the  existence  of  a  range  of 
choice,  it  is  worth  noting  that  some  of  the  optional  income- 
streams  would  never  be  chosen  under  any  circumstances. 
These  are  the  income-streams  the  present  value  of  which 
could  not  be  the  maximum,  no  matter  what  the  rate  of 
interest  might  be.  We  have  seen  that  the  land,  in  our 
example,  would  be  most  profitably  employed  for  farming, 
for  mining,  or  for  forestry,  according  to  the  rate  of  interest. 
But  it  would  not  be  employed,  let  us  say,  for  a  quarry,  no 
matter  what  might  be  the  rate  of  interest.  The  optional 
uses  which  are  thus  out  of  the  question  may  be  called 
ineligible.     We  need   consider   only  the   eligible  options. 


§  7  -  ^ 

The  six  conditions  for  determining  interest  just  enu- 
merated differ  from  those  given  in  the  preceding  chapter 
chiefly  by  the  introduction  of  number  four,  —  that  the  use 
of  capital  which  yields  the  maximum  present  value  will 


Sec.  7] 


SECOND  APPROXIMATION 


151 


be  selected.     This  additional  condition  is  of  so  much  impor- 
tance that  it  should  be  restated  in  two  other  forms. 

To  illustrate  these,  let  us  recur  to  the  example  of  the 
land,  which  could  be  used  in  any  one  of  three  ways.  We 
found  that  when  the  rate  of  interest  was  4  per  cent.,  the 
use  chosen  would  be  forestry,  as  this  possessed  the  greatest 
present  value.  If  we  now  compare,  year  by  year,  the  in- 
come from  the  land  when  used  for  forestry  purposes  with 
the  income  which  it  might  have  yielded  if  used  in  one  of 
the  other  ways,  —  as  farming,  —  we  shall  see  that  in  some 
years  there  is  an  excess  in  favor  of  the  forest  use,  and  in 
other  years  a  deficiency,  as  shown  in  the  following  table :  — 


Annual  Value  of  Uses  for 

Difference  in 
Favor  of 

Forest  Use 

Forestry 

Farming 

1st  year 

2d  year  

3d  year  

4th  year 

5th  year  

6th  year  

7th  year  

8th  year  

9th  year  

10th  year  

11th  year  

Each  year  after  .  .  . 

300 
400 
500 
500 
500 
500 
500 
500 
500 
500 

450 
450 
450 
450 
450 
450 
450 
450 
450 
450 
450 
450 

-450 
-450 
-150 
-50 
+  50 
+  50 
+  50 
+  50 
+  50 
+  50 
+  50 
+  50 

Here  we  see  that  for  the  first  four  years  there  is  a  com- 
parative disadvantage  or  sacrifice  (amounting  to  $450,  $450, 
$150,  $50  in  successive  years)  from  the  use  of  the  land  for 
forest  purposes  as  compared  with  farm  uses,  but  that  this 
disadvantage  is  made  up  later  by  an  advantage  or  return  of 
$50  per  annum.  If  we  now  take  the  total  present  value, 
at  4  per  cent.,  of  the  deficiencies  marked  with  a  minus  sign, 
we  shall  obtain  $1024,  whereas  the  present  value  of  the 
excesses  (continuing  in  perpetuity),  indicated  by  a  positive 


152  THE  RATE  OF  INTEREST  [Chap.  VIII 

sign,  will  be  $1070.  Thus  the  present  value  of  the  gains 
exceeds  the  present  value  of  the  sacrifices  by  the  difference 
between  $1070  and  $1024.  In  other  words,  as  reckoned  in 
present  estimation,  the  gains  outweigh  the  sacrifices.  We 
may  say,  therefore,  that,  the  rate  of  interest  being  4  per 
cent.,  forestry  is  preferable  to  farming  because  of  a 
surplus  of  advantages  over  disadvantages  reckoned  in 
present  value.  But  if  the  rate  of  interest  were  4^  per 
cent,  we  should  find  the  present  value  of  the  sacrifices 
to  be  $1017,  and  the  present  value  of  the  gains,  $930, 
showing  a  preponderance  of  the  sacrifices.  That  is,  if 
the  rate  of  interest  is  4^  per  cent.,  the  sacrifice  in  using 
the  land  for  forestry  rather  than  mining  outweighs  the 
gains.  The  land  would,  therefore,  in  that  case,  not  be  used 
for  forestry  purposes. 

The  general  principle  is,  therefore,  that  out  of  the  various 
income-streams  at  the  disposal  of  the  capitalist,  he  chooses 
the  mo.;t  advantageous,  or,  more  fully  expressed,  the 
one  which,  compaiod  with  any  other,  offers  advantages 
which,  reckoned  in  present  estimation  at  the  given  rate  of 
interest,  outweigh  the  disadvantages ;  and  this  is  evidently 
merely  a  new  formulation  of  the  original  principle  that  the 
use  chosen  will  be  that  which  has  the  maximum  present 
value  at  the  given  rate  of  interest. 

§8 

There  is  yet  a  third  method  of  stating  this  principle. 
This  method  may  also  best, be  shown  by  an  example.  We 
have  seen  in  the  previous  illustration  that  if  the  rate  of 
interest  is  4  per  cent.,  the  net  advantage  is  in  favor  of  the 
forest  use;  and  if  the  rate  of  interest  is  4^  per  cent.,  the 
advantage  is  in  favor  of  the  farming  use.  It  is  evident 
that  at  some  intermediate  rate  of  interest  the  comparative 
advantages  of  the  two  uses  would  be  equal.  This  inter- 
mediate rate  is  approximately  4.2  per  cent.  To  show  the 
nature  and  importance  of  such  an  equalizing  rate,  we  may 


Sec.  8] 


SECOND   APPROXIMATION 


153 


vary  the  example  given  to  the  following  simple  illustra- 
tion: — 


1st  year 
2d  year 
3d  year 
4th  year 
Each  subsequent  year 


Annual  Value  of  Uses  for 


Forestry 


000 
210 
100 
100 
100 


Farming 


100 
100 
100 
100 
100 


Difference  in 
Favor  of 
Forestry 


-100 

+  110 

000 

000 

000 


In  this  case  the  equalizing  rate  is  10  per  cent.  If  the  two 
income-streams  be  both  discounted  at  9  per  cent.,  the  for- 
estry use  will  have  the  greater  present  value,  $1112,  as 
against  $1111  for  the  farming  use.  If  11  per  cent,  is  used, 
the  scales  are  turned  and  the  farming  use  is  the  more  valu- 
able, being  worth  $909,  as  against  $908  for  the  forestry. 
At  the  intermediate  rate  of  10  per  cent.,  the  two  uses  are 
equivalent  in  present  value,  both  being  worth  exactly 
$1000.  Since  10  per  cent,  is  the  rate  which  equahzes  the 
advantages  and  disadvantages  of  the  two  alternatives  in 
present  value,  it  is  the  rate  at  which  the  third  column  in 
the  table  will  have  a  present  value  of  zero.  Again,  it  is 
the  rate  which  the  $110  yields  on  the  —$100,  or  the  rate 
"realized"  to  the  investor  who,  by  choosing  the  forestry 
use,  relatively  sacrifices  $100  this  year,  but  obtains  a  com- 
pensating return  of  $110  next  year.  Such  a  rate  is  therefore 
called  the  rate  of  return  on  sacrifice.  These  terms  are  ap- 
plied exclusively  to  the  comparative  merits  of  two  alter- 
native income-streams.  By  "sacrifice"  is  meant  the  com- 
parative loss  from  one's  income-stream  at  first,  caused  by 
substituting  one  use  of  capital  for  another ;  and  by  "  return  " 
is  meant  the  comparative  gain  which  later  accrues  by  rea- 
son of  this  same  substitution. 

To  return  to  the  original  example  and  the  table  in 
§  7,  the  equalizing  rate  was  4.2  per  cent.     This  was  the 


154  THE   RATE  OF  INTEREST  [Chap.  VIII 

rate  of  return  on  sacrifice  of  the  forestry  use  when  com- 
pared with  the  farming  use.  It  is  the  rate  which  makes 
the  series  of  future  returns,  $50,  $50,  etc.,  indefinitely, 
equivalent  in  present  value  to  the  first  sacrifices,  $450, 
$450,  $150,  and  $50.  It  follows  '  that  if  the  latter  series  of 
sums  were  successively  deposited  at  4.2  per  cent,  in  a  sav- 
ings bank,  they  would  "earn"  for  the  depositor  the  former 
series  of  sums.  In  short,  4.2  per  cent,  is  the  rate  which  an 
investor  "realizes"  who  in  the  first  four  years  sacrifices  suc- 
cessively $450,  $450,  $150,  and  $50,  and  receives  as  return 
in  succeeding  years,  $50,  $50,  etc.  In  general,  the  rate  of 
return  on  sacrifice  is  a  supposed  rate  of  interest  which 
will  make  equal  the  present  values  of  the  "  sacrifices " 
and  "returns"  involved  in  comparing  one  optional 
income-stream  with  another.  It  is  not,  of  course,  to  be 
confused  with  the  actual  rate  of  interest. 

Now  if  the  actual  rate  of  interest  is  4  per  cent.,  while 
the  rate  of  return  on  sacrifice  which  would  be  realized  by 
choosing  the  forestry  rather  than  the  farming  use  is  4.2 
per  cent.,  it  would  evidently  be  profitable  to  choose  forestry. 
As  the  investor  might  put  it,  he  would  be  getting  more  than 
the  market  rate,  — getting  4.2  per  cent,  instead  of  4  per 
cent.  If,  however,  the  rate  of  interest  in  the  market  is 
4.5  per  cent.,  it  would  not  pay  to  choose  the  forestry  use, 
for  to  do  so  would,  comparatively  to  the  farming  use,  re- 
turn only  4.2  per  cent.  In  this  case  the  prospective 
investor  would  evidently  prefer  to  choose  the  farming  use, 
and  then  lend  his  money  at  4.5  per  cent.  Recurring  to  the 
former  table,  we  see  that  had  he  chosen  the  forest  use 
instead  of  the  farming  use  he  would  have  sacrificed  during 
the  first  four  years  successively  $450,  $450,  $150,  and  $50. 
He  may,  if  he  likes,  put  these  very  sums  at  interest  in 
a  savings  bank  and  make  4.5  per  cent,  upon  them,  whereas, 
had  he  chosen  the  forest  use,  he  would  have  received  only 
4.2  per  cent.     In  other  words,  when  a  man  can  invest  at 

'  See  The  Nature  of  Capital  and  Income,  Chap.  XIII. 


Sec.  8]  SECOND  APPROXIMATION  155 

4,5  per  cent,  by  lending,  he  will  not  invest  at  4.2  per  cent, 
by  choosing  forestry  rather  than  farming. 

Out  of  all  possible  employments  of  his  capital,  the 
capitalist  will  choose  that  one  which,  compared  with  any 
other,  has  advantages  worth  the  disadvantages,  —  returns 
worth  the  sacrifices.  This  means  that  the  rate  of  return 
on  sacrifice  will  exceed  the  rate  of  interest. 

In  case  the  advantages  precede  the  disadvantages,  as 
when  the  merits  of  the  mining  use  are  compared  with  those 
of  the  farming  use,  the  proposition  must  be  reversed,  as 
follows :  The  earlier  advantage  will  be  chosen  only  in  case 
the  rate  of  later  sacrifice  on  present  return  is  less  than  the 
rate  of  interest.  In  such  a  case  it  would  be  more  conven- 
ient, in  comparing  the  two  uses,  to  regard  them  in  the 
opposite  order,  that  is  from  the  point  of  view  of  the 
advantages,  not  of  the  mining  use  over  the  farming  use, 
but  of  the  fanning  use  over  the  mining  use.  This  will 
make  the  sacrifices  precede  the  returns.  As  long  as  the 
sacrifices  always  precede  the  returns,  we  need  only  to  con- 
sider whether  or  not  the  rate  of  return  on  sacrifice  exceeds 
the  rate  of  interest.  If  it  does,|  the  optional  income- 
stream  which,  compared  with  another,  yields  such  return 
on  sacrifice  will  be  chosen  in  preference ;  otherwise  it  will 
be  rejected,^ 

*  Of  course  it  is  possible  to  have  two  alternative  uses  so  related 
that  the  sacrifices  are  not  grouped  together  in  one  mass  and  the  re- 
turns in  another,  but  are  intermingled.  Thus,  the  first  few  years 
may  offer  advantages,  the  following,  disadvantages,  those  following 
still  later,  advantages,  and  so  on  in  alternating  succession.  In  such 
a  case,  if  the  market  rate  of  interest  is  4  per  cent,  and  the  rate  which 
equalizes  the  gains  and  sacrifices  is  4.2  per  cent.,  in  order  to  decide 
which  of  the  optional  income-streams  ought  to  be  chosen,  it  would 
be  necessary  to  consider  the  effect  of  a  slight  variation  from  the  4.2 
per  cent,  rate  used  in  discounting  the  comparative  advantages  and 
disadvantages.  Let  the  rate  change  from  4.2  per  cent,  to  4.1  per 
cent.,  i.e.  toward  the  actual  rate  4  per  cent.  If  the  effect  of  such  a 
change  is  to  make  the  advantages  outweigh  the  disadvantages,  in 
present  value,  it  is  a  proof  that  the  income-stream  possessing  these 
advantages  and  disadvantages  is  preferable  to  the  one  being  com- 
pared with  it.     In  such   a  case  it  is  much  more  convenient  not  to 


156  THE  RATE  OF  INTEREST  [Chap.  VIII 

The  condition,  therefore,  determining  the  choice  between 
options  may  be  stated  in  any  one  of  three  ways,  namely: 
(1)  Out  of  all  options  that  one  is  selected  which  has  the 
maximum  present  value,  reckoned  at  the  market  rate  of 
interest;  (2)  Out  of  all  options  that  one  is  selected  of 
which  the  advantages  over  any  other  outweigh,  in  present 
value,  its  disadvantages,  when  both  are  discounted  at  the 
market  rate  of  interest ;  (3)  Out  of  all  options  that  one  is 
selected  which,  compared  with  any  other  option,  yields  a 
rate  of  return  on  sacrifice  greater  than  the  rate  of  interest. 


§  9 

Let  us  now  apply  the  third  mode  of  statement  to  the  case 
in  which  the  range  of  choice  is  not  confined  to  a  few  options, 
but  extends  to  an  infinite  number.  This  case  is  really 
more  like  the  facts  of  life  than  the  imaginary  case  of  a  few 
options,  such  as  the  farming,  mining,  or  forestry  uses  of 
land.  As  a  matter  of  fact,  each  of  these  is  not  a  single  use, 
but  a  whole  group  of  optional  uses.  Thus,  the  farmer  may 
cultivate  his  farm  with  any  degree  of  intensity;  and  for 
each  particular  degree  of  intensity  he  will  have  a  different 
income-stream.  He  may,  for  instance,  invest  $100  worth 
of  labor  in  the  present,  in  order  that  in  six  months  he 
may  have  a  larger  income  than  otherwise,  by  $200.  If  the 
rate  of  interest  is  4  per  cent,  (reckoned  semi-annually),  he 
would  evidently  prefer  this  option;  for  it  diminishes  his 
present  income  by  $100  and  increases  his  income  six  months 
later  by  $200,  being  100  per  cent,  in  six  months,  whereas  the 
interest  for  that  time  is  only  2  per  cent.  Another  course 
would  be  to  invest,  not  $100,  but  $200,  in  present  cultiva- 
tion. The  extra  $100  would  add  to  his  returns  in  a  half- 
year's  time  something  less  than  the  $200  yielded  on  his 

consider  at  all  any  equalizing  rate,  such  as  4.2  per  cent.,  but  to  recur 
to  one  of  the  preceding  methods.  In  practice,  however,  such  per- 
plexities seldom  or  never  arise. 


Sec.  9]  SECOND   APPROXIMATION  157 

first  $100,  let  us  say  $150.  This  also  would  be  a  good  in- 
vestment, yielding  him  50  per  cent,  return  when  the  rate 
of  interest  is  2  per  cent.  And  so  each  successive  choice, 
compared  with  its  predecessor,  shows  a  laiv  of  decreasing 
returns  for"  additional  sacrifice.  Thus,  if  he  invests,  not 
$200,  but  $300,  the  third  $100  thus  sacrificed  will  add  to 
his  returns  in  six  months,  let  us  say  $120.  Here  is  a  gain 
of  20  per  cent.,  whereas  the  rate  of  interest  is  only  2  per  cent. 
As  another  option,  he  may  sacrifice  a  fourth  $100  for  the 
sake  of  a  return  of  an  additional  $110;  in  like  manner  he 
may  sacrifice  a  fifth  $100  for  the  return  of  an  additional 
$105;  a  sixth  $100  for  an  additional  $103;  a  seventh  $100 
for  $102.  Thus  far,  each  successive  option  is  preferred 
to  its  predecessor;  for,  as  compared  with  its  predecessor, 
each  option  yields  more  than  2  per  cent.,  which  is  the  rate 
of  interest  for  six  months.  The  next  option  is  to  sacrifice 
an  eighth  $100  for  an  additional  $101  in  six  months. 
Evidently,  it  will  not  be  to  the  farmer's  interest  to  take 
this  last  step;  he  will  stop  at  the  previous  step,  at  which 
he  gets  a  2  per  cent,  return  on  the  last  sacrifice  of  $100. 
As  we  saw  in  the  preceding  section,  each  successive  option 
is  chosen  as  long  as  the  rate  of  return  on  sacrifice  of  that 
option,  compared  with  the  previous  option,  is  greater  than 
the  rate  of  interest,  and  that  use  is  rejected  at  which  the 
rate  of  return  on  sacrifice  becomes  less  than  the  rate  of  in- 
terest. The  mtensiveness  of  his  farming  is  thus  deter- 
mined by  the  rate  of  interest.  He  chooses  that  degree  of 
intensiveness  which  gives  his  income-stream  the  maximum 
present  value,  — which  is  the  same  thing  as  choosing  that 
degree  at  which  the  rate  of  return  on  sacrifice  is  equal 
to  the  rate  of  interest. 

The  various  possible  income-streams  are  represented  in 
Figure  17.  Income-stream  A  is  large  for  the  first  six 
months,  and  for  the  second  six  months  very  small.  The 
next  income-stream  B  is  $100  smaller  than  A  for  the 
first  six  months,  and  $200  larger  for  the  last  six  months. 
The  other  options  are  also  indicated.     Income-stream  H  is 


158 


THE  RATE  OF  INTEREST 


[Chap.  VIII 


the  one  chosen,  because,  as  compared  with  its  predecessor, 
its  disadvantage  is  $100  for  the  first  six  months  and  its 
advantage  $102  for  the  second  six  months  — just  enough 
to  "compensate  for  interest." 

We  therefore  reach  the  conclusion  that  where  the  options 
are  indefinite  in  number,  the  option  chosen,  compared  with  a 
neighboring  option  with  which  it  was  in  competition,  yields 
a  rate  of  return  on  sacrifice  equal  to  the  rate  of  interest. 


Fig.  17. 


This  rate  of  return,  computed  on  the  basis  of  two  alterna- 
tive income-streams  closely  neighboring  upon  each  other, 
we  shall  call  the  marginal  rate  of  return  on  sacrifice.  It 
follows  that,  when  there  is  a  continuous  range  of  choice,  we 
may  substitute  for  the  statement  that  the  choice  will  fall 
upon  the  option  of  maximum  present  worth,  the  better 
statement  that  the  choice  will  fall  on  the  option  whose 
marginal  rate  of  return  on  sacrifice,  reckoned  relatively  to 
a  neighboring  option,  is  equal  to  the  rate  of  interest. 


Sec.  10]  SECOND  APPROXIMATION  159 

§  10 

We  have  introduced  a  new  magnitude  into  our  discus- 
sion ;  namely,  the  rate  of  return  on  sacrifice,  and  especially 
the  particular  value  of  this  rate  of  return  called  the  mar- 
ginal rate  of  return  on  sacrifice.  This  marginal  rate  of 
return  on  sacrifice  comes  close  to  being  a  "natural  rate  of 
interest."  By  means  of  it  we  are  enabled  to  admit  into 
our  theory  the  elements  of  truth  contained  in  some  of  the 
claims  of  the  productivity  theories,  the  cost  theories,^  and 
Bohm-Bawerk's  theory  of  the  technique  of  production. 

The  example  just  given  of  the  farmer  who  selects,  out  of 
a  series  of  income-streams,  that  for  which  the  return  on  sac- 
rifice is  equal  to  the  rate  of  interest,  perfectly  exemplifies 
the  theory  of  John  Rae.^  According  to  Rae,  all  instru- 
ments may  be  arranged  in  an  order  depending  on  the 
rate  of  return  on  cost.  Some  instruments  return  double 
the  cost  of  their  formation  in  a  year;  in  other  words, 
the  rate  of  retm-n  on  sacrifice  is  100  per  cent.  Others 
return  50  per  cent.,  20  per  cent.,  and  so  on  in  descending 
order.  In  any  community,  Rae  says,  instruments  will  be 
"wrought  up"  to  the  point  at  which  the  rate  of  return  on 
sacrifice  corresponds  to  Rae's  equivalent  for  what  we  have 
called  the  "rate  of  preference,"  and  this,  in  turn,  as  we 
have  seen,  is  equal  to  the  rate  of  interest.  It  will  be  evi- 
dent to  every  student  of  Rae  that  the  preceding  discussion 
accords  with  Rae's  idea  that  those  instruments  which 
most  promptly  yield  returns  are  formed  first,  and  that  the 
less  rapidly  returning  instruments  are  successively  formed 
until  the  margin  is  reached  which  corresponds  to  the  rate 
of  interest.  The  statement  of  Rae  that,  for  a  certain  cost 
of  formation,  an  instrument  will  yield  a  certain  return,  is 
merely  a  form  of  our  statement  that  a  certain  decrease  of 
present  income  will  be  accompanied  by  a  certain  increase 

'  See  Rae,  The  Sociological  Theory  of  Capital,  Chapters  IV  to  VI. 
^Cf.  also  Landry,  L'InterH  du  Capital,  1904,  Chapter  III;  Carver, 
Distribution  of  Wealth,  New  York,  1904,  p.  230. 


160  THE  RATE  OF  INTEREST  [Chap.  VIII 

in  future  income.  The  relation  between  the  immediate 
decrease  and  the  futiu'e  increase  will  vary  within  a  wide 
range,  wherein  the  choice  will  fall  at  the  point  correspond- 
ing to  the  ruling  rate  of  interest. 

The  subject  is  one  which  may  be  looked  upon  from  many 
points  of  view,  and  it  is  important  that  these  points  of 
view  should  be  thoroughly  coordinated.  In  the  example 
above  given,  the  farmer  was  supposed  to  invest  to-day 
and  receive  retiu^ns  six  months  afterward.  Consider  now 
a  case  in  which  the  returns  are  repeated  regularly  each 
year.  Let  us  suppose  that  oiu*  farmer  possesses  some 
swamp  land  in  a  primitive  state.  He  has  a  large  range  of 
choice  as  to  the  method  of  utilizing  this  land.  He  can 
allow  it  to  remain  a  swamp  or,  by  clearing  and  draining 
it,  convert  it  into  crop-yielding  land,  the  yield  being  in 
proportion  to  the  thoroughness  with  which  the  clearing  and 
draining  are  accomplished.  Under  the  first  use,  let  us 
suppose  that  he  derives  a  perpetual  net  income  of  $50  a 
year,  and  let  us  suppose  that,  at  an  immediate  cost  of  $100 
for  clearing  and  draining,  he  can  secure  a  perpetual  net 
income  from  crops  of  $75  a  year.  As  between  these  two 
choices,  the  second  involves  a  decrease  of  immediate  in- 
come of  $100,  and  an  increase  in  annual  income  thereafter, 
from  $50  to  $75,  or  of  $25.  In  other  words,  the  invest- 
ment of  $100  will  yield  him  25  per  cent,  per  annum.  Evi- 
dently, if  the  rate  of  interest  in  the  market  is  5  per  cent., 
it  will  pay  him  to  make  such  an  investment.  Next  sup- 
pose that  a  second  $100  invested  in  improving  the  swamp 
would  cause  the  crop  retui'ns  to  be  $90  instead  of  $75  a  year, 
or  $15  more  than  before.  Evidently,  the  investment  of 
the  second  $100  yields  15  per  cent.,  and  is  also  a  lucrative 
one,  when  we  consider  that  the  rate  of  interest  is  only  5  per 
cent.  A  third  $100  may  increase  the  annual  crop  to  $100 
instead  of  $90,  an  excess  of  $10  as  compared  with  the 
previous  investment,  or  a  yield  of  10  per  cent.  A  fourth 
$100  invested  will  cause  the  annual  crop  to  be  $105,  giving 
an  increase  of  $5  and  a  yield  of  5  per  cent.     A  fifth  $100  will 


Sec.  11]  SECOND  APPROXIMATION  161 

cause  the  crop  to  increase  to  $108,  giviQg  an  increase  of  $3 
and  a  return  of  3  per  cent.  Evidently  it  will  pay  the  farmer 
to  invest  in  draining  and  improving  his  swamp  up  to  the 
fourth  $100,  but  not  to  the  fifth  $100.  Rather  than  invest 
this  fifth  $100  and  receive  thereon  an  annual  income  of  $3 
a  year,  he  would  prefer  to  invest  $100  in  the  savings  bank 
and  receive  5  per  cent,  a  year. 

In  other  words,  the  intensity  with  which  he  will  improve 
and  cultivate  his  land  is  determined  by  the  current  rate  of 
interest.  Should  the  rate  of  interest  in  the  market  fall  from 
the  5  per  cent,  just  assumed  to  2  per  cent.,  it  would  then 
pay  him  to  invest  the  fifth  $100.  For,  evidently,  if  need 
be,  he  could  borrow  $100  at  2  per  cent,  and  receive  from  his 
land  a  return  of  3  per  cent.  As  Rae  has  so  clearly  pointed 
out,  in  communities  where  the  rate  of  interest  is  low, 
swamps  will  be  more  thoroughly  improved,  roads  better 
made,  dwellings  more  durably  built,  and  all  instruments 
'* worked  up"  to  a  higher  degree  of  efficiency  and  a  lower 
marginal  return  than  in  a  community  where  the  rate  of 
interest  is  high. 

The  same  illustrations  which  have  been  given  will  serve 
to  set  the  present  theory  in  line  with  that  of  Adolphe 
Landry  in  his  Theorie  de  V  Interet.  He  states  that  one  of 
the  conditions  determining  the  rate  of  interest  is  the 
"productivity  of  capital,"  in  the  peculiar  sense  which  he 
gives  to  this  phrase.  The  process  described  by  Landiy 
by  which  the  productivity  is  assimilated  to  whatever  rate 
of  interest  happens  to  rule  the  market,  virtually  corre- 
sponds to  the  successive  selection  of  income-streams  as 
outlined  in  the  preceding  examples, 

§  11 
Our  next  case  will  serve  to  show  how  the  element  of 
truth  already  pointed  out  in  the  productivity  theory  of 
Del  Mar  and  George  fits  into  the  theory  here  propounded. 
This  theory  is  that  the  rate  of  interest  corresponds  to  the 
rate  of  growth  of  animals  and  plants.     In  Chapter  III  we 

M 


162 


THE  RATE  OF   INTEREST 


[Chap.  VIII 


saw  that  the  time  of  cutting  a  forest  will  be  that  at  which  it 
is  growing  at  a  rate  equal  to  the  rate  of  interest.  Thus,  if 
nine  years  from  the  planting  of  the  forest  it  contains  900 
cords  of  wood,  while  in  ten  years  it  contains  1000  cords, 
in  eleven  years,  1050,  and  in  twelve  years,  1071,  and  if  the 
rate  of  interest  is  5  per  cent.,  the  cutting  will  occur  between 
the  tenth  and  eleventh  years.  This  choice  is  determined 
by  precisely  the  same  principle  that  has  already  been 
emmciated;  namely,  that  the  particular  income-stream 
selected  will  be  that  which  has  the  maximum  present 
value;  or,  in  other  words,  that  which  is  such  that  the 
marginal  rate  of  return  on  sacrifice  will  be  equal  to  the 
rate  of  interest. 

To  show  how  this  principle  applies  to  the  cutting  of  the 
forest,  let  us  consider  as  the  first  option  the  cutting  of  the 
forest  at  the  end  of  nine  years,  when  the  income-stream 
consists  of  the  single  item, — the  production  of  900  cords 
of  wood.* 

The  second  option  is  cutting  the  forest  at  the  end  of  ten 
years,  and  receiving  an  income  item  of  $1000.  The  two 
alternatives  may  be  put  in  the  tabular  form  previously  em- 
ployed for  the  case  of  forestry  and  farming,  as  follows :  — 

OPTIONAL    INCOMES    FROM    FOREST 


10-Yeah 
Plan 

Q-Year 
Plan 

Difference 

IN  Favor  of 

10-Year  Plan 

1st  year     .... 
2d   year     .... 

000 
000 

000 
000 

900 
000 

9th  year     .... 
10th  year     .... 

000 
1000 

-    900 
+  1000 

'  Inasmuch  as  we  assume  that  the  income  from  the  forest  is  all  to 
accrue  at  one  time  —  the  time  of  cutting  —  instead  of  being  dis- 
tributed over  a  long  period,  the  phrase  "  income-stream  "  might  here 
better  be  replaced  by  "  income  item." 


Sec.  12]  SECOND  APPROXIMATION  163 

The  last  column  shows  that  the  ten-year  plan,  compared 
with  the  nine-year  plan,  involves  a  sacrifice  of  $900  in  the 
ninth  year  which  might  be  secured  by  the  nine-year  plan, 
but  involves  a  return  of  $1000  in  the  tenth  year.  The  rate 
of  return  on  sacrifice  would  thus  be  a  little  over  11  per 
cent.  If  the  rate  of  interest  in  the  market  is  5  per  cent., 
it  would  evidently  pay  to  "wait,"  or  to  choose  the  cutting 
in  the  tenth  year  rather  than  the  ninth  year. 

The  next  option  would  be  to  cut  in  the  eleventh  year, 
which,  as  compared  with  the  second  alternative,  would 
involve  a  sacrifice  of  $1000  in  the  tenth  year  and  a  return 
of  $1050  in  the  eleventh  year  —  in  other  words,  a  rate  of 
return  on  sacrifice  of  5  per  cent.  Evidently,  then,  it 
would  be  a  matter  of  indifference  whether  the  forest  was 
cut  in  the  tenth  or  eleventh  year,  inasmuch  as  the  rate  of 
return  on  sacrifice  in  one  alternative  as  compared  with  the 
other  would  be  exactly  equal  to  the  rate  of  interest. 

Similar  reasoning  shows  that  the  choice  of  the  next 
option,  that  of  cutting  the  forest  in  the  twelfth  year, 
would  yield  a  return  of  yf  iu,  or  2  per  cent.  Inasmuch  as 
2  per  cent,  is  less  than  the  rate  of  interest,  this  alternative 
would  be  rejected.  Should,  however,  the  rate  of  interest 
fall  to  2  per  cent.,  or  below,  it  is  clear  that  the  time  of  cutting 
the  forest  would  be  postponed  until  the  rate  of  increase 
in  stumpage  value  was  reduced  to  correspond  to  the  rate 
of  interest. 

§  12 

The  same  example  will  serve  to  show  the  bearing  of 
Bohm-Bawerk's  discussion  as  to  the  influence  of  the 
"roundabout  process"  upon  the  rate  of  interest.  Accord- 
ing to  him,  it  is  at  the  option  of  society  to  invest  to-day's 
labor  in  any  one  of  many  different  processes  bringing  re- 
turns in  different  lengths  of  time,  let  us  say,  nine  years,  ten 
years,  eleven  years,  etc.;  and  he  premises  that  the  returns 
in  these  successive  years  will  increase,  but  at  a  diminishing 


164  THE  RATE   OF   INTEREST  [Chap.  VIII 

rate,  let  us  say,  in  the  order  of  the  numbers  already  given : 
$900  for  the  ninth,  $1000  for  the  tenth,  $1050  for  the 
eleventh,  $1071  for  the  twelfth,  etc.  That  use  will  be 
selected,  as  Bohm-Bawerk  has  pointed  out,  which  has  the 
maximum  present  value;  and  also,  as  he  points  out,  the 
lower  the  rate  of  interest,  the  remoter  will  be  the  "produc- 
tion period"  on  which  the  choice  will  fall.  If  the  rate  of 
interest  is  5  per  cent.,  the  choice  will  fall  on  the  tenth 
or  eleventh  year;  if  the  rate  is  2  per  cent.,  on  the  eleventh 
or  twelfth  year;  and  the  lower  the  rate  of  interest  the 
more  "roundabout"  will  be  the  methods  of  production. 

This  is  entirely  valid  under  the  hypothesis  involved; 
namely,  that  there  is  a  range  of  optional  returns,  each 
consisting  of  a  definite  return  at  a  definite  point  of  time, 
increasing  as  the  production  period  increases,  but  at  a 
decreasing  rate.  It  is  also  true,  as  Bohm-Bawerk  has 
pointed  out,  that  not  only  does  a  lower  rate  of  interest 
tend  to  the  choice  of  remoter  returns,  but  that,  contra- 
riwise, the  choice  of  remoter  returns  tends  to  check  the 
fall  in  the  rate  of  interest;  the  reason,  expressed  in  our 
own  terminology,  being  that  the  choice  of  an  income- 
stream  relatively  large  in  the  future  and  small  in  the 
present  tends  to  increase  the  relative  valuation  of  present 
as  compared  with  future  income.  The  existence  of  such 
a  range  of  choice  as  Bohm-Bawerk  assumes,  therefore, 
tends  to  act  as  a  buffer,  checking  the  variations  in  the 
rate  of  interest.  This  effect  of  the  operation  of  a  range  of 
choice  will  be  again  referred  tb. 

§  13 

Thus,  the  elements  of  truth  which  were  found  in  the  pro- 
ductivity theory,  in  the  cost-theory,  and  in  Bohm-Bawerk's 
technique-of-production  theory,  all  find  a  place  under  the 
head  of  the  choice  among  optional  uses  of  capital.  In 
some  cases,  as  in  the  example  illustrating  the  theories  of 
Henry  George  and  Bohm-Bawerk,   the  selection  of  one 


Sec.  13]  SECOND  APPROXIMATION  165 

option  rather  than  another  involves,  as  its  effect  on  the 
income-stream,  the  mere  omission  of  one  item  of  income 
and  the  substitution  of  another.  In  other  cases,  as  in  the 
examples  illustrating  the  theory  of  John  Rae  and  Adolphe 
Landry,  the  selection  of  one  option  rather  than  another 
involves  the  application  of  labor,  or  the  incurring  of  cost 
of  some  other  sort,  for  the  sake  of  a  future  return.  But  in 
all  cases  there  is  a  choice  among  optional  income-streams, 
—  a  decision  how  to  adjust  the  income-stream  at  different 
periods,  whether  or  not  to  decrease  it  at  one  time  in  order  to 
increase  it  at  another.  It  matters  not  in  what  way  or  at 
what  periods  of  time  the  flexing  of  the  income-stream 
occurs.  It  may  be,  as  in  the  case  of  the  farmer  contem- 
plating the  planting  of  a  crop,  that  the  income  is  flexed 
or  varied  at  merely  two  points  of  time,  as  seed  time  and 
harvest;  or,  as  in  the  case  of  clearing  a  swamp,  there  may 
be  a  decrease  of  present  income  for  the  sake  of  an  increase 
of  the  income  of  all  succeeding  years;  or  there  may  be 
any  other  arrangement  of  sacrifices  and  returns.  But  in 
all  cases  we  have  to  deal  simply  with  a  range  of  choice 
among  income-streams  of  different  conformations.  If  this 
range  of  choice  were  limited  to  a  few  options,  the  best  state- 
ment of  the  principle  which  governs  the  selection  would  be 
that  the  income-stream  having  the  maximum  present  worth 
would  be  selected.  But  if  there  is  a  varied  or  continuous 
range  of  choice,  the  preferable  method  of  stating  the  prin- 
ciple is  that  the  income-stream  will  be  selected  which,  as 
compared  with  the  neighboring  streams,  will  yield  a  rate 
of  return  on  sacrifice  equal  to  the  rate  of  interest. 

To  a  person  who  has  never  tried  to  connect  them,  many 
of  the  theories  of  the  authors  just  compared  seem  to  have 
no  vital  relation.  But  they  are  seen  to  be  connected  as 
soon  as  we  look  at  them  in  the  light  of  the  concept  of  an 
income-stream.  The  problems  of  choosing  when  to  cut  a 
forest,  of  what  length  to  make  a  production  period,  to  what 
degree  of  intensiveness  to  cultivate  land,  or  how  far  to 
improve  a  piece  of  land,  are  all  problems  of  choosing  the 


166 


THE  RATE  OF  INTEREST 


[Chap.  VIII 


best  out  of  innumerable  possible  income-streams.  In  each 
problem  the  rival  income-streams  present  differences  as  to 
size,  shape,  composition,  or  probability,  —  especially  shape. 
In  respect  to  shape,  they  can  best  be  compared  by  means 


Fig.  18. 


of  diagrams.    Figures  18  to  21  show  typical  ways  in  which 
the  income-stream  may  conceivably  be  subjected  to  slight 


Fig.  19. 


variation.    The  unbroken  line  in  each  case  indicates  the 
income-stream  chosen,  and  the  dotted  line  a  neighboring 


Fig.  20. 


possible  choice.     Figure  18  may  be  taken  as  applying  to  the 
planting  of  a  crop ;  Figure  19  to  the  draining  of  a  swamp ; 


Fig.  21. 


Figure  20  to  the  cutting  of  a  forest ;  and  Figure  21  to  a 
case  of  alternating  sacrifices  and  returns. 


Sec.  14]  SECOND  APPROXIMATION  167 

To  students  of  physics,  it  will  be  interesting  to  obesrve 
that  the  identity  of  the  principle  of  maximum  present 
value  with  the  principle  that  the  marginal  rate  of  return 
on  sacrifice  is  analogous  to  the  identity  between  the  prin^ 
ciple  of  minimum  energy  and  D'Alembert's  principle.  A 
suspension  bridge  assumes  the  form  which  will  bring  its 
center  of  gravity  at  the  lowest  possible  point ;  this  is  in 
accordance  with  the  principle  of  minimum  energy.  It  is 
clear  that  the  various  parts  of  the  structure,  so  to  speak, 
compete  with  each  other  in  the  effort  each  to  reach  the 
lowest  possible  point.  The  result  is  a  compromise;  no 
part  reaches  the  lowest  point  for  itself  but  is  held 
above  it  by  the  sagging  of  other  parts.  If  from  the 
position  of  equilibrium  a  slight  displacement  of  any  de- 
scription is  imagined,  it  requires  that  the  depression  of 
some  parts  is  offset  by  the  elevation  of  others,  the  work 
being  done  by  the  one  set  being  equal  to  that  done  upon 
the  other  set ;  this  is  in  accordance  with  the  principle  of 
D'Alembert  (principle  of  virtual  displacements).  The 
income- curve  is  like  the  curve  of  the  hanging  bridge  re- 
versed. The  effort  is  to  raise  it  as  high  as  possible  so  that 
its  present  value  is  a  maximum.  But  its  various  parts 
compete  with  each  other  in  the  attempt  each  to  reach  the 
point  highest  in  present  value.  The  result  is  a  compro- 
mise; no  part  reaches  the  highest  value  possible  for  itself 
but  is  kept  from  so  doing  by  the  other  parts.  If  from  the 
position  of  equilibrium  a  slight  displacement  of  any  de- 
scription is  imagined,  it  requires  that  the  elevation  of  some 
parts  is  offset  by  the  depression  of  others,  the  present 
value  of  the  gains  being  equal  to  the  present  value  of  the 
losses.  This  is  equivalent  to  saying  that  the  rate  of  re- 
turn on  sacrifice  is  equal  to  the  rate  of  interest. 

§  14 

Up  to  this  point  one  complication  in  the  problem  of 
interest  has  been  carefully  kept  in  the  background,  not 


168  THE  RATE  OF  INTEREST  [Chap.  VIII 

because  it  invalidates  any  of  the  principles  which  have  been 
developed,  but  because  it  seemed  advisable  not  to  distract 
attention  from  the  essential  features  of  the  theory  by  intro- 
ducing prematurely  a  factor  which,  after  all,  is  more  intri- 
cate than  important.  This  compHcation  consists  in  the 
fact  that  not  only,  as  we  have  seen,  does  the  choice  between 
different  optional  income-streams  depend  upon  the  rate  of 
interest,  but  also  that  even  the  range  of  choice  depends  upon 
that  rate.  If  the  rate  of  interest  is  changed,  a  change  is 
produced  not  only  in  the  present  values  of  the  income- 
streams  but  in  the  income-streams  themselves.  To  recur 
to  the  illustration  of  the  land  which  may  be  devoted  to  one 
of  three  uses,  not  only  is  it  true  that  a  change  in  the  rate 
of  interest  from  5  per  cent,  to  4  per  cent,  will  change  the 
relative  present  values  of  the  income-streams  which  consist 
of  the  farming,  mining,  and  forestry  uses  of  the  land,  but 
this  change  from  5  per  cent,  to  4  per  cent,  may  also 
materially  affect  the  three  income-streams  themselves. 

The  net  income  from  any  instrument  of  wealth  is  the 
difference  between  the  total  gross  income  and  the  outgo. 
But  many  of  the  elements,  both  of  income  and  outgo,  are 
materially  dependent  upon  the  rate  of  interest.  Tliis  is 
true,  whether  the  items  of  income  and  outgo  are  "final" 
or  merely  "intermediate."  ^  In  the  case  of  intermediate 
income,  or  "interactions,"  a  change  in  the  rate  of  interest 
affects  the  income-stream  directly,  because,  as  has  been 
shown  elsewhere,^  the  valuation  of  an  interaction  involves 
the  discoimt-process  and  is  therefore  dependent  upon  the 
rate  of  interest.  Thus,  the  service  of  planting  apple  trees 
will  be  valued  in  part  by  discounting  the  value  of  the  fu- 
ture apples.  Given  the  value  of  the  apples,  it  is  evident  that 
the  value  of  the  planting  will  be  high  or  low  according  as 
the  discounting  is  reckoned  at  a  low  or  a  high  rate  of  in- 
terest. But  even  "final"  income  —  the  income  secured 
from  the  apples,  for  instance  —  may  be  indirectly  affected 

*  See  The  Nature  of  Capital  and  Income,  Chaps.  VII-X. 
^  Ibid.,  p.  317. 


Sec.  14]  SECOND   APPROXIMATION  169 

by  a  change  in  the  rate  of  interest,  through  a  redistribu- 
tion in  the  amounts,  combinations,  and  values  of  the  vari- 
ous items  constituting  final  income,  and  hence  in  their 
values. 

It  would  lead  us  aside  from  our  topic  to  follow  these  lines 
of  reasoning  to  the  limit.  It  will  suffice  to  indicate  in  brief 
their  application  in  the  case  of  labor.  The  labor  cost 
is  one  of  the  commonest  elements  of  outgo  in  the  income- 
account  connected  with  any  group  of  capital.  For  in- 
stance, whether  the  land  is  used  for  farming,  mining,  or 
forestry,  it  must  be  worked  by  human  beings,  and  the 
cost  of  the  work  will  materially  affect  the  values  of  the  three 
income-streams.  Now  the  cost  of  that  work  is  wages,  and, 
to  the  employer,  takes  the  form  of  and  normally  represents 
the  discounted  value  of  the  ultimate  enjoyable  services  to 
which  the  labor  leads.  Consequently,  if  interest  varies, 
wages  will  vary.  Thus,  if  the  land  is  used  for  farming, 
the  wages  paid  for  planting  crops  will  be  gauged  in  the 
estimation  of  the  farmer  by  discounting  the  value  of  the 
expected  crops,  and  will  vary  somewhat  according  as  the 
discounting  is  at  5  per  cent,  or  4  per  cent.  In  like  man- 
ner, the  workers  engaged  in  bridge  building  are  paid  the 
discounted  value  of  the  ultimate  benefits  which  will  accrue 
after  the  bridge  is  built;  the  wages  of  those  engaged  in 
making  locomotives  normally  represent  the  discounted  value 
of  the  completed  locomotives,  and  hence  (as  the  value  of 
a  completed  locomotive  is  in  turn  the  discounted  value  of 
its  expected  services)  their  wages  represent  the  discounted 
value  of  the  ultimate  benefits  in  the  series.  In  all  these 
cases,  the  rate  of  wages  is  the  discounted  value  of  some 
future  product,  and  therefore  tends  to  decrease  as  interest 
increases.  But  the  effects  in  the  different  lines  will  be  very 
unequal.  Workers  whose  product  matures  rapidly,  as  in 
the  case  of  domestic  servants  and  in  the  case  of  those  en- 
gaged in  putting  the  finishing  touches  on  enjoyable  goods, 
will  have  their  wages  comparatively  little  affected  by  the 
rate  of  interest.     On  the  other  hand,  for  laborers  who  are 


170  THE  RATE  OF  INTEREST  [Chap.  VIII 

engaged  in  work  requiring  much  time,  the  element  of  dis- 
count applied  to  their  wages  is  a  much  more  important 
factor.  If  a  tree  planter  is  paid  $1  because  this  is  the 
discounted  value,  at  5  per  cent.,  of  the  $2  which  the  tree 
will  be  worth  when  matured  in  fifteen  years,  it  is  clear 
that  a  change  in  the  rate  of  interest  to  4  per  cent,  will 
tend  materially  to  raise  the  value  of  such  labor.  Sup- 
posing the  value  of  the  matured  tree  still  remains  at  $2, 
the  value  of  the  services  of  planting  it  would  be,  not  $1, 
but  $1.15.  On  the  other  hand,  for  laborers  engaged  in  a 
bakery  or  other  industry  in  which  the  final  satisfactions 
mature  early,  the  wages  are  almost  equal  to  the  value  of 
these  products.  If  they  produce  final  services  worth  $1, 
due,  let  us  say,  in  one  year,  their  wages,  being  the  dis- 
counted value  of  this  sum  at  5  per  cent,  per  annum,  would 
be  95  cents.  Evidently  in  such  a  case  a  change  in  the 
rate  of  interest  from  5  per  cent,  to  4  per  cent,  would  only 
increase  the  wages  from  95  cents  to  96  cents. 

But  it  is  clear  that  such  unequal  effects  coming  from  a 
reduction  in  the  rate  of  interest,  as  an  increase  from  $1 
to  $1.15  in  one  industry,  and  from  95  cents  to  96  cents 
in  another,  could  not  remain  permanently.  For  the 
laborers  engaged  in  the  occupations  in  which  their  work 
matured  in  a  relatively  short  time,  such  as  the  bakers  just 
mentioned,  finding  that  their  neighbors  engaged  in  lengthier 
processes  were  receiving  higher  wages,  would  tend  to  desert 
their  work  for  this  more  remunerative  employment.  The 
consequence  would  be  that  the  amount  of  labor,  and  con- 
sequently the  amount  of  final  enjoyable  income,  accruing 
from  the  shorter  processes  would  be  reduced,  and  that 
from  the  longer  processes  increased.  The  consequence  of 
this,  in  turn,  would  be  to  raise  the  value  of  the  earlier 
enjoyable  income  and  lower  that  of  the  later.  Therefore, 
in  the  end,  the  change  in  the  rate  of  interest  from  5  per  cent, 
to  4  per  cent,  would  effect  a  redistribution  in  the  values,  not 
only  of  intermediate  items  of  income,  but  in  the  values  of 
the  final  items  themselves.     For  the  various  final  elements 


Sec.  15]  SECOND  APPROXIMATION  171 

of  income  are  bound  together,  as  it  were,  by  means  of  the 
competition  of  the  preparatory  services,  such  as  those  of 
the  laborers  just  mentioned,  and  the  consequent  neces- 
sity of  equaUzing  the  remuneration  for  these  preparatory 
services. 

In  short,  a  change  in  the  rate  of  interest  will  affect  all 
income-streams  flowing  from  given  instruments  of  capital 
whether  these  streams  consist  of  interactions  or  of  final 
services.  It  will  affect  (1)  the  value  of  interactions,  like 
tree-planting  or  bread-baking,  because  the  rate  of  interest 
enters  directly  into  the  valuation  of  all  interactions;  and 
(2)  the  value  of  final  income,  enjoyments,  because  many  in- 
teractions, as,  for  instance,  the  services  of  laborers,  may 
be  used  interchangeably  in  several  different  directions. 
Tlie  effect  of  a  change  in  the  rate  of  interest,  on  the 
value  of  the  interactions,  will  naturally  be  the  more  pro- 
nounced, and  will  be  greater  in  a  country  where  lengthy 
processes  are  usually  employed  than  in  one  where  the 
shorter  ones  are  common.  If,  for  instance,  laborers  in  a 
given  country  are  engaged  largely  in  building  elaborate 
works  like  the  Panama  Canal,  in  planting  forests,  and 
otherwise  investing  for  the  sake  of  remote  returns,  a  fall 
in  the  rate  of  interest  will  produce  a  considerable  rise  in 
wages;  whereas,  in  a  country  where  such  lengthy  pro- 
cesses are  unknown  and  workmen  are  chiefly  employed 
in  tilling  the  ground  and  performing  personal  services,  a 
change  in  the  rate  of  interest  will  scarcely  affect  wages 
and  the  values  of  other  preparatory  services  at  all. 

§  15 

The  complete  discussion  of  this  subject  would  lead  us 
to  a  statement  of  the  general  theory  of  the  "price  of  labor" 
and  of  prices  in  general.  For  present  purposes,  it  is 
only  necessary  to  emphasize  the  bare  fact  that  the  range 
of  choice  between  different  income-streams  is  somewhat 
dependent  upon  the  rate  of  interest.    If  the  modification 


172 


THE  RATE  OF  INTEREST 


[Chap.  VIII 


due  to  this  fact  were  introduced  into  the  tables  previously 
given  for  the  three  different  uses  of  land,  we  should  find 
that  the  income-streams  from  using  the  land  for  farming, 
forestry,  and  mining  would  differ  according  to  the  rate  of 
interest. 

Thus,  let  us  suppose,  as  before,  that  for  a  rate  of  interest 
of  5  per  cent,  the  three  optional  income-streams  are :  — 


1st  year 
2d  year 
3d  year 
4th  year 
5th  year 
6th  year 
7th  year 
8th  year 
9th  year 
10th  year 
Thereafter 


Forestry 


000 
000 
300 
400 
500 
500 
500 
500 
500 
500 
500 


Farming 


Mining 


450 

2000 

450 

1800 

450 

1600 

450 

1400 

450 

1200 

450 

1000 

450 

800 

450 

600 

450 

400 

450 

200 

450 

000 

In  our  previous  discussion,  when  we  changed  the  rate  of 
interest  from  5  per  cent,  to  4  per  cent.,  we  supposed  the 
figures  in  this  table  to  remain  unchanged.  The  only  change 
we  had  then  to  deal  with  was  the  change  in  their  present 
values.  Now,  however,  we  admit  the  possibility  of  a 
change  in  the  table  figures  themselves.  If  the  rate  of 
interest  falls  to  4  per  cent.,  the  product  of  forest,  farm,  and 
mine  will  be  more  nearly  equal  to  the  value  of  the  ultimate 
services  to  which  they  lead.  The  value  of  lumber  will  be 
more  nearly  equal  to  the  value  of  the  houses  it  makes,  and 
these  to  the  value  of  the  shelter  they  give;  the  value  of 
wheat  from  a  farm  will  be  nearer  the  value  of  the  bread  it 
will  make ;  and  the  value  of  ore  from  a  mine  will  be  nearer 
the  value  of  the  steel  it  will  become,  and  this,  in  turn,  more 
nearly  equal  to  the  values  of  those  innumerable  satisfac- 
tions which  come  through  the  use  of  steel.  These  shif tings 
forward  of  the  values  of  the  intermediate  income  of  forest, 


Sec.  15] 


SECOND   APPROXIMATION 


173 


farm,  and  mine  toward  the  values  of  the  ultimate  satis- 
factions to  which  they  lead,  combined  with  possible  read- 
justments in  the  values  of  these  satisfactions  themselves 
— the  values  of  house  shelter,  bread  consumption,  etc. — 
will  result  in  a  change,  say  in  the  figures  in  the  table  from 
those  just  given  for  5  per  cent,  to  the  following  for  4  per 
cent. :  — 


1st  year 
2d  year 
3d  year 
4th  year 
5th  year 
6th  year 
7th  year 
8th  year 
9th  year 
10th  year 
Thereafter 


Forestry 


000 
000 
350 
450 
600 
600 
600 
600 
600 
600 
600 


Farming 


Mining 


500 

2100 

500 

1900 

500 

1700 

500 

1500 

500 

1300 

500 

1100 

500 

850 

500 

650 

500 

450 

500 

225 

500 

000 

If,  then,  the  rate  is  5  per  cent.,  the  landowner  will  choose 
that  use  among  the  three  which,  computing  from  the  figures 
in  the  first  table,  has  the  greatest  present  value;  while  if 
the  rate  is  4  per  cent.,  he  will  choose  that  which,  computing 
from  the  figures  in  the  second  table,  has  the  greatest  present 
value.  If,  then,  the  rate  is  5  per  cent.,  he  will  choose  min- 
ing, since,  as  we  saw  in  §  4,  the  present  values,  when  we 
compute  at  5  per  cent.,  are :  forestry,  $8820 ;  farming,  $9000 ; 
mining,  $9110;  but  if  the  rate  is  4  per  cent.,  he  will  choose 
the  highest  from  the  present  values  at  4  per  cent.,  computed 
from  the  second  table.  Tliese  present  values  now  are: 
forestry,  $13,520;  farming,  $12,500;  mining,  $10,100. 
Thus  the  owner  will  choose  forestry.  It  is  true  in  this 
case  that  the  change  in  the  range  of  choice  does  not  affect 
the  final  result.  In  §  4  the  choice  also  fell  on  the 
forestry  use.    The  only  difference  is  that  the  particular 


174  THE  RATE  OF  INTEREST  [Chap.  VIII 

figures  of  present  values  in  our  revised  4  per  cent,  com- 
putation are  different  from  their  values  in  our  original 
4  per  cent,  computation.  The  present  values  at  4  per 
cent,  for  forestry,  farming,  mining,  respectively :  — 

Under  our  present  hypothesis  are  13,520  12,500  10,100 
Under  our  former  hypothesis  were         11,300         11,250  9,450 

But,  whatever,  the  final  outcome  of  all  the  readjust- 
ments, it  is  evident  that  the  introduction  of  the  in- 
fluence of  the  rate  of  interest  on  the  range  of  choice 
does  not  in  any  material  way  affect  the  reasoning  already 
given  in  regard  to  the  determination  of  interest.  Since  the 
rate  of  interest  will  itself  fix  the  range  of  choice,  it  will 
still  be  true  that,  once  the  range  of  choice  is  fixed  for  a 
given  rate  of  interest,  the  individual  will  choose,  as  before, 
that  use  which  has  the  maximum  present  value.  On  the 
basis  of  this  choice  he  is  then  led  to  borrow  or  lend  in  order 
to  modify  his  income-stream  so  that  his  rate  of  time-prefer- 
ence may  harmonize  with  the  rate  of  interest.  If,  upon  an 
assumed  rate  of  interest,  the  borrowing  and  lending  for 
different  individuals  actually  cancel  one  another,  — •  in 
other  words,  clear  the  market,  —  then  the  rate  of  interest 
assumed  is  clearly  the  one  which  solves  the  problem ;  other- 
wise the  borrowing  and  lending  will  not  be  in  equilibrium, 
and  some  other  rate  of  interest  must  be  selected.  By  suc- 
cessively postulating  different  rates  of  interest,  and  remem- 
bering that  each  rate  carries  with  it  its  own  range  of  options 
and  its  own  set  of  present  values  of  those  options,  we  finally 
obtain  that  one  which  will  clear  the  market. 

We  therefore  conclude  by  repeating,  slightly  modified, 
the  formulation  of  the  theory  stated  in  §6:  (1)  Each 
individual  has  given  a  specific  list  of  eligible  optional 
income-streams  (some  of  which  depend  upon  the  rate  of 
interest) ;  (2)  The  rate  of  preference  for  each  individual 
depends  upon  the  character  of  his  income-stream ;  (3)  All 
the  individual  rates  of  preference  are,  through  the  loan  or 
sale  market,  equalized  with  one  another  and  with  the  rate 


Sec.  16]  SECOND  APPROXIMATION  175 

of  interest;  (4)  Each  individual  selects,  out  of  the  range 
of  choice  of  income-streams  available  at  a  given  rate  of 
interest,  that  particular  one  which  has  the  maximum  present 
value,  —  in  other  words,  that  one  whose  advantages  over 
any  other  outweigh  (in  present  value)  its  disadvantages, — 
or,  in  still  other  words,  that  one  which  compared  with 
others  makes  the  rate  of  return  on  sacrifice  greater  than 
the  rate  of  interest,  —  or,  finally  (if  the  options  are  in- 
finitely numerous),  that  one  which  compared  with  neigh- 
boring options  makes  the  marginal  rate  of  return  on 
sacrifice  equal  to  the  rate  of  interest;  (5)  The  demand 
and  supply  of  loans  must  balance  for  each  period  of  time ; 
and  (6)  The  loans  returned  must  equal  the  loans  obtained, 
with  interest. 

§16 

Having  completed  the  formal  statement  of  the  effect  of 
the  existence  of  a  range  of  choice  upon  the  rate  of  interest, 
it  remains  to  point  out  a  practical  effect  of  such  a  range  of 
choice.  Tills  effect  is  to  diminish  the  fluctuations  in  the 
rate  of  interest.  In  a  country  where  there  is  a  large  range 
of  choice  between  optional  income-streams,  the  rate  of 
interest  is  apt  to  be  steadier  than  in  one  where  the  income 
streams  are  relatively  rigid  and  unalterable.  If  any 
cause  tends  to  lower  the  rate  of  interest,  the  immediate 
effect  will  be  to  put  a  premium  on  those  income-streams 
the  return  from  which  is  in  the  remote  future, — for 
instance,  to  put  a  premium  on  forestry  uses  rather  than 
mining  uses  of  land.  But  the  decision  to  choose  such  in- 
come-streams tends  to  prevent  the  very  fall  in  the  rate  of 
interest  which  caused  the  choice.  For,  by  relatively  over- 
supplying  the  future  with  income,  and  undersupplying  the 
present,  such  uses  as  forestry  will  tend  to  raise  the  relative 
valuation  of  present  over  future  income,  and  therefore 
also  to  raise  the  rate  of  interest.  The  fall,  therefore,  in 
the  rate  of  interest  which  led  to  the  choice  of  remoter  in- 


176  THE  RATE   OF  INTEREST  [Chap.  VIII 

comes,  is  checked,  and  is  not  so  great  as  it  would  be  if  no 
such  options  were  open. 

Conversely,  a  rise  in  the  rate  of  interest  will  favor  those 
options  for  which  the  income-streams  are  relatively  im- 
mediate, and  wiU  bring  its  own  check;  for  the  choice  of 
such  an  income-stream  wiU  relatively  impoverish  remote 
income  and  enrich  immediate  income,  and  consequently 
tend  to  diminish  the  premium  on  the  latter. 

The  existence  of  a  large  nmnber  of  available  income- 
streams,  then,  acts  as  a  balance  wheel  which  tends  to 
check  any  excessive  changes  in  the  rate  of  interest.  In- 
terest cannot  fall  or  rise  unduly ;  for  any  such  fluctuation 
corrects  itself  through  the  choice  of  appropriate  income- 
streams.  If  interest  is  high,  descending  income-streams 
will  be  chosen  which  tend  to  make  interest  low;  while, 
if  it  is  low,  the  reverse  will  be  true. 

We  see  here  another  reason,  m  addition  to  those  given 
in  Chapter  VII,  for  the  fact  that  interest  does  not  suffer 
very  violent  fluctuations.  It  is  not  only  true,  as  was  then 
pointed  out,  that  natm-al  processes  are  regular  enough  to 
prevent  sudden  and  great  changes  in  the  income-stream; 
but  it  is  also  true  that  man  constantly  aims  to  prevent  such 
changes.  Man  is  not  the  slave  of  Natiu-e's  income;  to  some 
extent  he  is  her  master.  He  has  many  options  among 
which  he  may  choose.  He  possesses,  within  limits,  the 
power  to  flex  his  income-stream  to  suit  himself.  For 
society  the  flexibility  is  due  to  the  adaptability  and  ver- 
satility of  capital,  — especiaUy  human  capital  commonly 
called  labor ;  for  the  individual  the  flexibility  is  greater  stiU, 
since  he  possesses  a  double  range  of  choice.  He  may 
not  only  choose  among  different  employments  of  capital, 
but  he  mav  choose  among  different  wavs  of  exchanging 
with  other  people,  — he  may  borrow  or  lend,  buy  or  seU, 
invest  or  spend.  This  power  is  virtually  the  power  to 
trade  in  income;  for  under  whatever  form  an  exchange 
takes  place,  at  bottom  it  is  income,  and  income  only,  which 
is  exchanged.     In  making  his  choice  among  different  em- 


Sec.  16]  SECOND  APPROXIMATION  177 

ployments  of  capital,  he  relies  on  his  power  to  remedy 
any  undesirable  time-shape,  etc.,  by  recourse  to  exchange. 
The  result  of  the  double  range  of  choice — that  between 
optional  employments  of  capital  and  betwx'en  optional 
modes  of  exchanging  income  —  is  that  his  income  is 
flexible  and  controllable  in  a  high  degree.  Xot  only  may 
he  select  the  most  valuable  income,  but  also  the  income 
which  is  most  desirable  in  respect  to  time-shape.  lie  need 
not  even  commit  himself  to  a  given  time-shape  for  any 
great  length  of  time,  for  by  changing  his  expenditures  and 
investments  he  can  alter  that  time-shape  at  wih.^ 

•  For  further  discussion  of  the  subject  of  this  chapter  by  means  of 
mathematics,  see  Appendix  to  Chap.  VIII. 


N 


CHAPTER  IX 

CLASSES   OF  OPTIONS 
§1 

In  order  to  present  a  full  view  of  what  is  meant  by 
"optional  employments  of  capital,"  it  will  be  worth  our 
while  to  pause  a  moment  and  examine  the  different  classes 
of  options  open  to  the  capitalist. 

Options  are  of  three  chief  kinds:  (1)  options  among  em- 
ployments of  capital  which  differ  in  kind,  as,  for  instance, 
the  options  previously  cited  of  using  land  for  mining, 
farming,  or  forestry ;  (2)  options  among  employments  of 
capital  which  differ  in  the  degree  of  certainty,  as,  for  in- 
stance, the  choice  of  sailing  a  ship  over  several  routes 
differing  in  the  constancy  of  wind  and  current;  and 
(3)  options  among  employments  of  capital  which  differ 
in  size  and  time-shape. 

Options  of  the  first  group  do  not  concern  the  theory  of 
interest  so  much  as  the  theory  of  prices,  unless,  as  in  the 
example  of  the  mining,  farming,  and  forestry  uses  of  land, 
the  optional  incomes  differ  in  time-shape  as  well  as  in  the 
kind  of  service  rendered.  This  gi'oup  may  be  designated  as 
options  of  versatility.  They  are  most  striking  in  the  case 
of  tools  and  human  beings. 

Options  of  the  second  class  may  be  called  options  of 
chance.  They  concern  the  theory  of  insurance  and  spec- 
ulation rather  than  the  theory  of  interest,  and,  under  the 
hypothesis  which  has  thus  far  been  maintained,  that  risk 
is  absent,  have  no  need  as  yet  to  be  considered.  This 
group  of  options  is,  however,  of  great  practical  importance. 
Under  this  head,  when  the  options  relate  to  contractual 

178 


Sec.  1]  CLASSES  OF  OPTIONS  179 

services,  comes  the  special  case  of  trade  options.  It  is  to 
this  class  that  the  term  "option"  is  ordinarily  applied 
by  business  men,  and  it  has  been  with  some  hesitation 
that  it  has  been  given  a  broader  meaning  in  this  book. 
But  no  better  term  seems  available;  and  there  is  to  be 
said,  in  favor  of  the  broader  use  of  the  word,  that  it  corr 
responds  closely  to  its  popular  and  untechnical  meaning. 

The  third  group  of  options  is  the  one  which  specially 
concerns  us  here,  and  will  alone  engage  our  attention 
through  the  remainder  of  this  chapter, 
'  When,  in  Chapter  VII,  we  explicitly  excluded  optional  em- 
ployments of  capital,  we  thereby  assumed  that  the  income- 
stream  was  fixed  both  in  amount  and  in  the  times  when  it 
accrued.  We  may  pass  from  this  case  of  perfect  rigidity 
to  the  simplest  form  of  option  by  introducing  at  first  only 
one  degree  of  flexibility.  Let  us  suppose  that  the  income- 
stream  from  any  capital  is  relatively  fixed  in  amount,  and 
that  only  the  time  of  obtaining  it  is  controllable  at  will. 
Tliis  species  of  choice  occurs  in  the  case  of  durable  goods 
for  consumption,  which  neither  improve  nor  deteriorate 
with  time.  Wheat  and  other  grains,  for  instance,  may 
be  used  at  almost  any  time,  with  little  difference  in  the 
efficiency  of  the  use  and  little  cost  except  for  storage. 
The  same  is  true  of  coal,  cloth,  iron,  and  other  durable 
raw  materials,  as  weU  as,  to  some  extent,  of  finished  prod- 
ucts such  as  tools  and  machinery,  though  usually  de- 
terioration from  rust  or  other  injury  by  the  elements 
will  set  in  if  the  use  is  too  long  deferred. 

Where  such  a  range  of  choice  exists,  the  possibility  of 
obtaining  an  income  from  the  capital  in  the  future  instead 
of  in  the  present  will  have  the  effect  of  preventing  the  rate 
of  interest  from  sinking  as  far  as  it  otherwise  would ;  for  if 
the  rate  of  interest  is  low,  the  tendency  on  the  part  of  the 
investor  will  be  to  defer  the  use  of  durable  goods,  —  wheat, 
for  instance,  —  and  such  a  decision,  by  increasing  future 
income  and  diminishing  immediate  income,  will  tend  to 
raise  the  rate  of  interest,  or  at  least  to  check  its  fall.     Re- 


180  THE  RATE  OF  INTEREST  [Chap.  IX 

versely,  the  possibility  of  using  such  articles  at  the  present 
time  instead  of  later  has  the  effect  of  preventing  the  rate 
of  interest  from  rising  as  far  as  it  otherwise  would ;  for, 
should  interest  rise,  the  tendency  on  the  part  of  the  investor 
will  be  to  more  immediate  employment  of  such  durable 
goods  as  he  had  set  apart  for  futm'e  use,  and  this  decision, 
by  relatively  increasing  present  income  and  diminishing 
future  income,  will  tend  to  reduce  the  rate  of  interest,  or, 
at  any  rate,  to  check  its  rise.  Tliis  is  illustrated  by  wheat 
speculation.  A  rise  in  the  rate  of  interest  will  check 
"bull"  operations,  since  the  speculator  will  be  less  will- 
ing to  "lose  the  interest  on  his  money."  Reversely,  when 
the  rate  of  interest  falls,  wheat  holding  will  be  encouraged. 
Likewise  land  speculation  is  relatively  easy  when  interest 
is  low  and  difficult  when  interest  is  high. 

§2 

Under  the  group  of  options  applying  to  durable  in- 
struments, there  are  many  special  cases.  One  of  the 
most  instructive  is  that  which  we  might  suppose  if  the 
quantity  of  income  obtainable  from  an  instrument  or  num- 
ber of  instruments  were  definitely  fixed,  but  the  time  at 
which  those  services  might  be  obtained  were  entirely 
optional.  To  illustrate  this,  uncomplicated  by  the  pres- 
ence of  instruments  of  different  types  and  the  consequent 
necessity  to  translate  the  rate  of  interest  into  a  common 
monetary  standard,  let  us  imagine  a  community  in  which 
the  income  from  all  capital  is  of  the  character  just  de- 
scribed. This  society  would  then  be  endowed  with  a 
quantum  of  income  as  fixed  as  the  quantity  of  money  in  a 
strong  box.  It  could  obtain  all  the  income  at  once,  or 
spread  it  over  any  number  of  years,  but  could  not  alter 
its  amount  either  by  increase  or  decrease,  just  as  the  owner 
of  a  strong  box  could  take  the  contents  all  out  at  once, 
or  at  such  times  as  he  pleased,  but  could  not  increase  or 
diminish  the  total  amount.     Every  dollar's  worth  of  income 


Sec.  2]  CLASSES  OF  OPTIONS  181 

sacrificed  from  this  year's  income  would  eke  out  next  year's 
income  by  a  dollar  and  no  more;  and  reversely,  every 
dollar's  worth  indulged  in  this  year  would  reduce  by  a 
dollar  and  no  more  the  possibility  of  future  indulgence. 

Let  us  suppose  this  case  realized  on  a  desert  island  on 
which  some  sailors  are  shipwrecked  and  left  each  with  1000 
pounds  of  hardtack  and  no  prospect  of  ever  improving  their 
lot.  We  will  suppose  the  use  of  this  hardtack  to  be  the 
only  "real  income"  open  to  these  castaways,  and  that  they 
have  given  up  hope  of  ever  adding  to  it  by  accessions  from 
outside  or  by  cultivating  the  island  (which,  by  our  hypothe- 
sis, must  be  barren),  the  only  possible  variation  of  their 
income-stream  —  consisting  of  hardtack  — being  that  pro- 
duced by  varying  the  time  of  its  consumption.  They  have 
the  option  of  consuming  their  entire  store  during  the  first 
year,  or  of  spreading  its  use  over  two  or  more  years, 
but  in  any  case  they  will  have  the  same  total  income, 
measured  in  hardtack.  A  little  reflection  will  show  that 
in  such  a  commimity  the  rate  of  interest  in  terms  of  hard- 
tack would  necessarily  be  zero.^  For,  by  hypothesis,  the 
sacrifice  of  one  pound  of  hardtack  unconsumed  from  this 
year's  income  can  only  result  in  an  equal  increase  in  the 
income  of  future  years.  Therefore  the  rate  of  return  on  sac- 
rifice is  zero.  Since  this  rate  must  equal  the  rates  of 
preference  and  the  rate  of  interest,  these  rates  must  all 
be  zero  also. 

To  illustrate  this  case  by  a  diagram,  we  see,  as  one  op- 
tion, that  the  entire  consumption  of  hardtack  may  take  place 
at  an  even  rate  OA  within  the  time  OB  (Fig.  22).  The  total 
income  will  then  be  represented  by  the  area  OACB.  An- 
other option  is  that  it  shall  be  spread  over  OB',  double  the 
above-mentioned  time,  and  consumed  at  the  rate  0A\ 
half  the  rate  first  mentioned,  so  that  the  same  total 
amount  will  be  represented  by  the  area  OA'C'B'.  The 
choice   of   the  second   use   rather  than  the  first   implies 

'  Cf.  Adolphe  Landry,  L'InterH  du  Capital,  p.  49;  Carver,  The  Dis- 
tribution of  Wealth,  p.  232. 


182 


THE  RATE  OF  INTEREST 


[Chap.  IX 


the  sacrifice  of  that  part  of  the  immediate  income  repre- 
sented by  the  rectangle  AD,  but  the  addition  of  equal 
future  income  represented  by  the  rectangle  DB'.    If  the 


hardtack  is  not  consumed  at  a  uniform  rate,  the  optional 
income-streams  will  not  be  represented  by  rectangles,  but 


Fig.  23. 


by  sloping  curved  figures,  as  ADB  and  A'DB'  (Fig.  23), 
which  have  the  same  area.     The  substitution  of  the  alter- 


Sec.  2]  CLASSES  OF  OPTIONS  183 

native  A'DB'  for  ADB  increases  immediate  income  by 
ADA'  and  decreases  subsequent  income  by  the  exactly 
equal  amount  BDB'. 

The  conclusion  that  the  rate  of  interest  under  such  con- 
ditions must  be  zero,  is  at  first  startling ;  but  it  is  easy  to 
convince  ourselves  of  its  correctness  if  we  reflect  that  the 
sailors  will  modify  the  time-shape  of  their  respective  income- 
stream  until  any  possible  rate  of  preference  for  a  present 
over  a  future  allowance  of  hardtack  disappears.  It  would 
be  impossible  for  any  would-be  lender  to  obtain  interest  on 
his  loan,  for  the  only  way  in  which  a  borrower  could  repay 
a  loan  would  be  to  pay  it  out  of  his  original  stock  of  hard- 
tack. He  would  not  be  fool  enough  to  borrow  100  pounds 
to  consume  to-day  and  pay  back  105  pounds  at  the  end  of 
a  year,  when  he  had  the  option  to  consume  the  100  pounds 
of  his  own  hardtack,  by  sacrificing  only  100  pounds  out 
of  his  own  stock  kept  for  next  year.  Consequently 
there  could  be  no  interest  payable  in  any  exchange  of 
present  for  future  hardtack.  It  is  equally  impossible  that 
there  should  be  a  negative  rate  of  interest.  No  one  would 
lend  100  pounds  of  hardtack  to-day  for  95  receivable  a 
year  later,  when  he  had  the  option  of  simply  storing  away 
his  100  pounds  to-day  and  taking  it  out  undiminished  a  year 
later.  Hence,  exchanges  of  present  for  future  hardtack 
could  not  exist,  except  at  par.  There  could  be  no  premium 
or  discount  in  such  exchange. 

Nor  could  there  be  any  rate  of  preference  for  present 
over  future  hardtack.  A  pound  of  this  year's  hardtack  and 
a  pound  of  next  year's  hardtack  would  be  equally  balanced 
in  present  estimation ;  for,  should  a  man  prefer  one  rather 
than  the  other,  he  would  take  a  pound  for  the  preferred 
use  away  from  the  unpreferred,  and  this  process  would  be 
continued  until  the  desirability  (in  the  present)  of  a  pound 
of  immediate  hardtack  and  that  of  a  pound  of  future  hard- 
tack were  brought  into  equilibrium.  Thus,  if,  through 
insufficient  self-control,  he  foolishly  prefers  to  use  his  store 
freely  in  the  present  and  to  cut  down  his  reserve  for  the 


184  THE  RATE  OF  INTEREST  [Chap.  IX 

future  to  a  minimum,  the  very  scantiness  of  the  provision 
for  the  future  will  enhance  his  appreciation  of  its  claims, 
and  the  very  abundance  of  his  provision  for  the  present 
will  diminish  the  urgency  of  his  desire  to  indulge  so  freely 
in  the  present.  Provided  there  is  some  hardtack  for  both 
uses,  the  present  desire  for  a  pound  of  each  will  necessarily  be 
the  same.  Failure  of  such  equilibrium  of  desire  can  only 
occur  when,  as  in  starvation,  the  desire  for  the  present  use 
is  so  intense  as  to  outweigh  the  desire  for  even  the  very  last 
pound  for  future  use,  in  which  case  there  will  be  none 
whatever  reserved  for  the  future.  But  whether  the  hard- 
tack is  at  first  abundant  — for  instance,  enough  to  insure 
a  long  life  —  or  whether  starvation  will  necessarily  follow 
after  a  year  or  two,  the  needs  of  the  present  and  future  will 
be  adjusted  on  a  basis  of  par  price  up  to  a  point  of  time  when 
the  income-stream  will  cease.  It  is  evident  that  some  of 
the  sailors,  with  a  keen  appreciation  of  the  future, 
would  plan  to  consume  their  stores  sparingly.  Others 
would  prefer  generous  rations,  even  with  the  full  knowl- 
edge that  starvation  would  thereby  ensue  earlier;  but 
none  of  them  would  consume  all  of  their  stock  immediately, 
for  to  do  so  would  unduly  rob  the  future,  already  poorly 
provisioned.  They  would,  generally  speaking,  prefer  to 
save,  out  of  such  reckless  waste,  at  least  something  to  satisfy 
the  more  urgent  needs  of  the  future.  In  other  words,  a 
certain  amount  of  saving  (if  such  an  operation  can  be  called 
saving)  would  take  place  without  any  interest  at  all.  This 
coincides  with  conclusions  expressed  by  Professor  Carver 
in  his  Distribution  of  Wealth.^  It  shows  also  that  the 
preference  for  present  over  future  goods  of  like  kind  and 
number  is  not,  as  some  writers  seem  to  assume,  a  neces- 
sary attribute  of  human  nature,  but  that  it  depends 
always  on  the  relative  provisioning  of  the  present  and  the 
future. 

*  p.  232.  See  also  "The  Place  of  Abstinence  in  the  Theory  of  In- 
terest," Quarterly  Journal  of  Economics,  July,  1894,  and  Fetter's 
Principles  of  Political  Economy,  New  York  (Century),  1904,  p.  160. 


Sec.  3]  CLASSES  OF  OPTIONS  185 

§   3 

The  fact  that  interest  was  bound  to  be  zero  in  the  case  of 
the  sailors  just  discussed,  was  due  to  the  extreme  adjust- 
abiUty  of  the  time  of  receiving  the  given  income.  To  see 
this  clearly,  let  us  next  consider  the  case  of  an  income-stream 
which,  as  before,  is  of  a  fixed  amount,  and  the  times  of 
receiving  which,  though  capable  of  being  postponed  as  far 
as  desired,  are  not  capable  of  being  hastened  beyond  a  cer- 
tain limit;  the  income,  in  other  words,  is  fixed  and  sure, 
but  comes  slowly.  Approximately  such  a  case  is  found  in 
mining.^  The  total  yield  of  a  mine  is  practically  fixed  by 
the  ore  deposits  which  it  contains.  It  is  like  the  chest  of 
money;  just  so  much  as  it  contains  can  be  taken  from  it, 
and  no  more.  But  it  is  unlike  the  chest  of  money  in  that 
its  contents  cannot  be  extracted  as  fast  as  desired.  The 
ore  at  the  top  must  be  removed  before  that  beneath  can  be 
reached.  Time  for  mining  operations  is  required.  Nature 
is  slow  in  yielding  up  her  treasures.  This  sloumess  of 
Nature,  in  view  of  man's  impatience  to  exploit  her,  will  give 
rise  to  a  rate  of  interest. 

It  is  as  though  the  hardtack  of  our  shipwrecked  sailors 
had  in  some  way  been  stored  in  a  series  of  storehouses,  each 
provided  with  a  time  lock  arranged  to  open  at  a  certain 
date.  There  is  a  definite  amount  of  income,  but  it  is  only 
available  at  intervals.  Under  these  circumstances,  unless 
the  time  locks  are  timed  to  open  as  fast  as  the  castaways 
would  have  chosen  of  themselves  to  eat  their  stores,  the 
hardtack  of  to-day  and  of  next  year  will  no  longer  exchange 
at  par.  There  will  be  a  premium  on  present  hardtack  as 
compared  with  future  hardtack,  the  amount  of  the  premium 
depending  on  the  relative  provisioning  of  the  various 
storehouses,  —  in  short,  on  the  size  and  time-shape  of  the 

*  Strictly  speaking,  of  course  the  total  product  and  total  expense 
of  exploiting  a  mine  will  vary  somewhat  with  the  rate  of  extraction. 
An  animated  discussion  of  the  most  profitable  rate  of  extraction  was 
carried  on  in  The  Engineering  and  Mining  Journal,  New  York,  1904. 


186  THE  RATE  OF  INTEREST  [Chap.  IX 

income-stream  as  made  available  by  the  time  locks.  The 
case  will  be  practically  the  same  as  though  the  income- 
stream  were  rigid,  as  in  Chapter  VII ;  for  the  only  option  is 
to  postpone  the  consumption  of  these  provisions,  and  this 
option  would  not,  under  the  circumstances,  be  exercised. 
We  see,  therefore,  that  in  order  that  a  positive  rate  of 
interest  shall  emerge,  it  is  only  necessary  that  income  shall 
sufficiently  hold  back  its  flow.  It  is  not  necessary  that 
Nature  should  be  reproductive,  as  Del  Mar  and  George 
maintain.  Interest  would  exist  even  if  there  were  no 
growing  animals  and  plants,  but  only  a  world  of  minerals 
and  other  fixed  stores  to  be  extracted  by  man,  provided 
only  Nature  were  slower  than  we  could  wish  in  admitting 
us  to  her  stores.  In  fact,  if  we  were  asked  to  state  in  a  word 
why  there  is  interest,  we  should  reply,  because  Nature  is 
slow  and  keeps  man  waiting. 

§  4 

But  while  the  slowness  of  Nature  is  a  sufficient  cause  for 
interest,  her  productivity  is  an  additional  cause.  This 
brings  us  to  our  next  class  of  options,  the  class,  namely, 
in  which,  if  present  income  is  sacrificed  for  the  sake  of  future 
income,  the  amount  of  the  latter  secured  thereby  is  greater 
than  that  of  the  former  sacrificed.  The  income  which  we 
can  extract  from  our  planet  is  not,  in  the  aggregate,  a 
fixed  quantum,  as  is  that  part  of  it  which  comes  from  mines, 
but  is  obtainable  in  larger  amounts  for  the  remote  future 
than  for  the  present.  Nature  is  reproductive  and  tends  to 
multiply.  Growing  crops  and  animals  make  it  possible  to 
endow  the  future  more  richly  than  the  present.  By  waiting, 
man  can  obtain  from  the  forest  or  the  farm  more  than  he 
can  by  premature  cutting  or  the  exhaustion  of  the  soil. 
In  other  words,  not  only  the  slowness  of  Nature,  but  also 
her  productivity  or  growth,  has  a  strong  tendency  to  keep 
up  the  rate  of  interest.  Nature  offers  man,  as  one  of  her 
optional  income-streams,  the    possibility  of   great  future 


Sec.  5]  CLASSES  OF  OPTIONS  187 

abundance  at  trifling  present  sacrifice.  This  option  acts 
as  a  bribe  to  man  to  sacrifice  present  income  for  futm-e,  and 
this  tends  to  make  present  income  scarce  and  future  income 
abundant  and  hence  also  to  create  in  his  mind  a  prefer- 
ence for  a  unit  of  present  over  a  unit  of  future  income. 

§  5 

We  next  consider  the  case  of  an  option  the  exact  reverse 
of  the  preceding,  — the  case  in  which,  if  present  income  is 
sacrificed,  the  amount  of  future  income  obtained  thereby 
is  less  than  the  amount  sacrificed  to  obtain  it.  This  is 
true  of  the  income  from  perishable  goods. 

Suppose  our  sailors  were  left,  not  with  a  stock  of  hard- 
tack, but  with  a  stock  of  figs  which  deteriorate  at  the  fore- 
known rate  of  50  per  cent,  per  annum.  In  this  case  the  rate 
of  interest  would  be  necessarily  minus  50  per  cent,  per 
annum,  as  may  be  shown  by  the  same  reasoning  that  es- 
tablished the  zero  rate  in  the  former  case.  The  possibility 
of  such  negative  interest  has  been  discussed  in  a  previous 
chapter.^  When  goods  are  perishable  the  tendency  is  to 
preserve  them  by  cold  storage,  preservatives,  etc.,  so  as  to 
extend  their  use  into  the  future.  This  is  an  effort  to  create 
a  new  optional  employment  for  those  goods. 

Some  goods,  then,  like  grain  for  food,  and  cloth,  may  be 
indiscriminately  applied  to  the  present  or  future  without 
either  loss  or  gain ;  others,  like  grain  for  seed,  breeding 
animals  and  plants,  gain  in  income  power  with  time;  and 
still  others,  like  meat  and  fruit,  lose. 

The  resultant  is  that,  for  income  as  a  whole,  taking  man 
and  Nature  as  they  are,  it  is  impossible  to  sacrifice  future  in- 
come for  present  very  far  without  selling  one's  birthright 
for  a  mess  of  pottage,  or,  to  make  use  of  another  phrase- 
ology, without  killing  the  goose  that  lays  the  golden  egg. 
Thus  Nature,  by  her  productivity,  stimulates  man  to  self- 
denial,  and  by  her  slowness  she  compels  it.     Were  the 

»  Chap.  V,  §  5. 


188  THE  RATE  OF   INTEREST  [Chap.  IX 

world  in  which  we  hve  neither  slow  nor  reproductive,  but 
simply  an  open  storehouse  of  wealth,  two  things  would 
happen  which  we  saw  in  the  case  of  the  shipwrecked 
sailors.  One  is  that  the  rate  of  interest  would  be  zero,  and 
the  other  is  that  man,  however  frugally  he  consumed  his 
stores,  must  ultimately  perish. 

§  6 

In  the  foregoing  cases  the  options  consisted  of  different 
employments  of  instruments  of  capital  which  were  assumed 
to  retain  their  physical  identities  throughout  the  period 
of  those  employments.  If  now  we  regard  an  instrument 
or  group  of  instruments  of  capital  as  retaining  its  identity 
through  renewals  or  repairs,  we  introduce  another  large  and 
important  class  of  options;  namely,  the  options  of  making 
those  renewals  and  repairs,  or  not  making  them,  or  making 
them  in  any  one  of  many  different  degrees.  If  the  repairs 
are  just  sufficient  for  the  up-keep  they  may  be  called  re- 
newals ;  if  more  than  sufficient,  they  may  be  called  better- 
ments. We  shall  include  all  these  alterations  wrought 
upon  an  instrument  in  the  same  category.  They  are 
alterations  in  the  form,  position,  or  condition  of  an 
instrument  or  group  of  instruments  which  affect  the  stream 
of  services  which  that  instrument  or  group  will  yield. 
This  class  of  optional  employments,  when  the  employment 
of  the  capital  involves  sales,  merges  imperceptibly  into  the 
special  case  which  we  originally  called  the  method  of  modi- 
fying an  income-stream  by  buying  or  selling.  Thus, 
consider  a  merchant  who  buys  and  sells  rugs.  His  stock 
of  rugs  is  conveniently  regarded  as  retaining  its  identity, 
although  the  particular  rugs  in  it  are  continually  changing. 
This  stock  yields  its  owner  a  net  income  equal  to  the  dif- 
ference between  the  gross  income,  consisting  of  the  pro- 
ceeds of  sales,  and  the  outgo,  consisting  chiefly  of  the  cost 
of  purchases,  but  including  also  cost  of  warehousing,  in- 
surance, wages  of  salesmen,  etc.     If  the  merchant  buys 


Sec.  6]  CLASSES  OF  OPTIONS  189 

and  sells  equal  amounts  of  rugs  and  at  a  uniform  rate,  his 
stock  of  rugs  will  remain  constant  and  its  income  to  be 
credited  to  that  stock  will  normally  be  equal  to  the  in- 
terest upon  its  value.  It  will  be  standard  income.^  But 
the  owner  has  many  options.  He  may  choose  to 
enlarge  his  business  as  fast  as  he  makes  money  from 
it,  in  which  case  his  net  income  will  be  zero  for  a 
time,  but  his  stock  will  increase  and  his  ultimate  in- 
come will  be  larger.  In  this  option,  therefore,  his  income- 
stream  is  not  constant,  but  ascends  from  zero  to  some  figure 
above  the  "standard  income"  of  the  first  option.  A  third 
option  is  gradually  to  go  out  of  business,  by  buying  less 
rugs  than  are  sold,  or  none  at  all.  In  this  case  the  income 
at  first  is  very  large,  as  it  is  relieved  of  the  burden  of  pur- 
chases; but  it  declines  gradually  to  zero.  In  the  inter- 
stices between  these  three  options  there  are,  of  course, 
endless  intermediate  options.  The  merchant  thus  has  a 
very  flexible  income-stream.  If  the  expenses  and  receipts 
for  each  rug  bought  and  sold  are  the  same  whichever  option 
is  chosen,  and  if  the  time  of  turnover  is  also  the  same,  it 
wiU  follow  that  all  of  the  options  possess  the  same  present 
value  and  differ  only  in  desirability.  We  should  then  be 
dealing  with  that  special  class  of  options  which  we  found 
open  even  in  the  case  of  rigid  income-streams,  —  what  we 
then  called  modifications  of  the  income-stream  through 
buying  and  selling.  The  reason  for  placing  optional 
employments  of  capital  on  a  different  footing  is  that  they 
do  not  all  possess  the  same  present  value.  In  actual  fact, 
the  rug  merchant,  and  merchants  in  general,  would 
not  find  that  all  the  optional  methods  of  proportion- 
ing sales  and  purchases  of  merchandise  possessed  equal 
present  values;  for  if  he  attempted  to  enlarge  his  business 
too  fast  he  would  find  that  his  time  of  tm-nover  would  be 
lengthened,  and  if  he  reduced  it  too  fast  he  would  find  that 

'  The  case  of  evenly  reconstituted  capital  is  emphasized  in  J.  B. 
Clark's  writings,  e.g.  The  Distribution  of  Wealth.  New  York  (Mac- 
millan),  1899;  see  The  Nature  of  Capital  and  Income,  Chap.  XIV,  §  4. 


190  THE  RATE  OF  INTEREST  [Chap.  IX 

his  selling  expenses  per  unit  of  merchandise  would  be  in- 
creased. There  is  for  each  merchant,  at  any  time,  one 
particular  line  of  business  policy  which  is  the  best ;  namely, 
that  which  will  yield  him  the  income-stream  having  the 
maximum  present  value.  It  is  his  interest  to  choose  this 
policy  and  to  relieve  himself  of  any  resulting  inconvenience 
in  the  time-shape  of  his  income-stream  by  borrowing  and 
lending  or  by  buying  and  selling.  Since,  therefore,  the 
various  methods  of  renewing  one's  capital  usually  yield 
income-streams  differing  in  present  value,  they  resemble 
what  we  have  called  optional  employments  of  capital  and 
may  be  properly  classed  as  such. 


The  propriety  of  such  a  classification  becomes  still  more 
evident  when,  instead  of  renewals,  we  consider  repairs  and 
betterments;  for  it  is  clear  that  the  income  from  a  farm 
has  a  very  different  present  value  according  as  it  is  tilled 
or  un tilled,  or  tilled  in  different  degrees  of  intensity ;  that 
the  income  from  a  house  so  neglected  that  a  leak  in  the 
roof  or  a  broken  window  pane  results  in  injuring  the  in- 
terior is  less  valuable  than  the  income  it  would  yield  if 
properly  kept  up;  and  that  real  estate  may  be  under- 
improved  or  overimproved  as  compared  with  that  degree 
of  improvement  which  secures  the  best  results. 

In  all  cases  the  best  results  are  secured  when  that  series  of 
renewals,  repairs,  or  improvements  is  chosen  which  renders 
the  present  value  of  the  prospective  income-stream  a  maxi- 
mum. This,  as  we  have  seen,  is  tantamount  to  saying  that 
the  renewals,  repairs,  or  improvements  are  carried  up  to  the 
point  at  which  the  return  which  they  bring  is  equal  to  the 
rate  of  interest.  The  owner  of  a  carriage,  for  instance,  will 
replace  a  broken  spoke,  because  the  cost  of  doing  so  will  pro- 
long the  life  of  his  carriage  so  far  as  to  earn  much  more  than 
the  interest  upon  the  trifling  cost  of  the  spoke.  This  repair 
may  cost  him  $1  and  may  save  him  $20.     But  so  high  a 


Sec.  8]  CLASSES  OF  OPTIONS  191 

rate  of  return  as  these  figures  imply  cannot  be  expected 
from  every  repair,  and  after  the  really  necessary  repairs 
are  made,  it  soon  becomes  a  question  to  what  extent  it  is 
worth  while  to  keep  a  carriage  in  repair.  Repainting,  re- 
varnishing,  and  resetting  the  tires  are  all  costly,  and  though 
in  every  case  the  service  of  the  carriage  is  increased  in  quan- 
tity and  improved  in  quality,  the  return  grows  less  and 
less  as  the  owner  strives  after  increased  efficiency.  He  will 
spend  money  on  his  carriage  in  repairs  and  renewals  up 
to  that  point  where  the  last  increment  of  repairs  will  secure 
a  return  which  will  just  cover  the  cost  with  interest; 
beyond  this  he  will  not  go. 

§  8 

Another  case  of  optional  income-streams  is  found  in  the 
choice  between  different  methods  of  production,  especially 
between  different  degrees  of  what  has  been  called  "capital- 
istic" production.  It  is  always  open  to  the  prospective 
housebuilder  to  build  of  stone,  wood,  or  brick ;  to  the  pro- 
spective raihoad  builder  to  use  steel  or  iron  rails ;  to  the 
maker  of  roads  to  use  macadam,  asphalt,  wood,  cobble, 
brick,  etc.,  or  to  leave  the  earth  unchanged  except  for  a 
little  hardening  and  rolling.  The  choice  will  in  all  cases 
depend  on  the  principles  which  have  been  already  explained. 

For  another  example,  the  services  of  a  house  which  has 
a  durability  of  60  years  will,  compared  with  one  which  has 
a  durability  of  30  years,  be  equivalent  to  the  services  of 
two  houses,  one  built  to-day  and  lasting  30  years,  and  the 
other  built  at  the  expiration  of  that  period  and  lasting  30 
years  more.  The  difference  between  the  one  long-lived 
house  and  the  two  short-lived  houses  is  thus  not  in  the 
services,  but  in  the  cost  of  construction.  The  cost  of  con- 
structing the  60-year  house  occurs  in  the  present;  that 
of  the  two  successive  30-year  houses  occurs  haff  in  the 
present  and  half  at  the  end  of  30  years.  In  order  that 
the  more  durable  house  may  have  the  advantage  as  to 


192  THE  RATE  OF  INTEREST  [Chap.  IX 

cost,  the  excess  of  its  cost  over  the  cost  of  the  first  of  the 
less  durable  ones  must  be  less  than  the  present  value  of 
the  cost  of  the  second,  deferred  30  years. 

The  choice  between  different  instruments  for  effecting 
the  same  purpose  may,  of  course,  depend  on  their  relative 
efficiency,  —  the  rate  of  flow  of  income,  or  upon  their 
lelative  durability,  —  the  time  of  the  flow.  It  is  true, 
however,  as  Jolm  Rae  has  pointed  out,^  that  efficiency 
and  durability  usually  go  hand  in  hand.  A  house  which 
will  endiu-e  longer  than  another  is  usually  more  comfort- 
able also ;  a  tool  which  will  cut  better  will  wear  out  more 
slowly;  a  machine  which  does  the  fastest  work  will  gen- 
erally need  to  be  strong  and  therefore  lasting. 

The  alternatives  constantly  presented  to  most  business 
men  are  between  policies  which  may  be  distinguished  as 
temporary  and  permanent.  The  temporary  involves  the 
use  of  easily  constructed  instruments  which  soon  wear  out, 
and  the  permanent  policy  involves  the  construction  at  great 
cost  of  instruments  of  great  durability.  When  one  method 
of  production  requires  a  greater  cost  at  first  and  yields  a 
greater  return  afterward,  it  may,  conformably  to  popular 
usage,  be  called  the  more  "capitalistic"  of  the  two.  In 
other  words,  "capitalistic"  methods  of  employing  capital 
are  those  which  tend  toward  an  ascending  income-stream. 
The  title  "capitalistic"  is  not  a  happy  one,  although  it  has 
some  justification  in  the  fact  that  an  ascending  income- 
stream  means  the  accumulation  of  capital,  or  "saving," 
and  still  more  in  the  fact  that  only  a  capitalist  can  afford 
to  choose  a  method  of  production  which  at  first  yields  little 
or  no  income,  or  even  costs  some  outgo ;  for  without  cap- 
ital no  one  could  subsist,  or  at  any  rate  subsist  with  comfort, 
in  the  interim.  It  is  clear  that  the  capitalist  who  thus 
subsists  on  his  accumulations  does  so  by  possessing,  or  be- 
coming possessed  of,  a  descending  income-stream.  It  is 
therefore  as  a  possessor  of  income  that  he  is  enabled  to 
subsist  while  waiting  for  the  returns  from  his  new  venture. 

'  The  Sociological  Theory  oj  Capital,  p.  47. 


Sec.  9]  CLASSES  OF  OPTIONS  193 

He  is  enabled  to  invest  in  an  ascending  or  slowly  return- 
ing income-stream  by  having  at  command  a  descending  or 
quickly  returning  income-stream.  We  may  say,  therefore, 
that  a  "capitalistic"  method  is  a  method  requiring  an 
ascending  income-stream,  and  it  is  so  called  because  it  is 
open  only  to  those  who  have  command  of  other  and 
descending  income-streams,  such  persons  being  necessarily 
capitalists. 

§  9 

The  best  example  of  the  choice  between  those  uses  of 
capital  affording  immediate  and  those  affording  remote 
returns  is  found  in  the  case  of  human  capital,  commonly 
called  labor.  Man  is  the  most  versatile  of  all  forms  of 
capital,  and  among  the  wide  range  of  choices  as  to  the  best 
disposition  of  his  energies  is  the  choice  between  using  them 
for  immediate  or  for  remote  returns.  This  choice  usually 
carries  with  it  a  choice  between  corresponding  uses  of 
other  instruments  than  man.  To  choose  to  plant  a  tree  for 
the  sake  of  fruit  ten  years  hence,  rather  than  to  plant  corn 
for  the  sake  of  next  year's  crop,  is  to  make  choice  of  differ- 
ent uses  of  land  as  well  as  of  labor.  But  the  existence  of 
optional  employments  of  labor,  however  inextricably  bound 
up  with  optional  employments  of  other  instruments, 
deserves  mention  both  because  of  its  importance  and  be- 
cause it  usually  supplies  the  basis  for  the  optional  employ- 
ments of  other  forms  of  capital. 

It  is,  in  fact,  almost  exclusively  through  varying  the 
emplojmient  of  labor  that  the  income-stream  of  society 
as  a  whole  is  capable  of  changing  its  time-shape.  The 
individual  may  modify  the  time-shape  of  his  particular 
income-stream  through  exchange,  but  in  this  case  the  person 
who  exchanges  with  him  must  modify  his  income-stream  in 
the  opposite  manner,  and  the  two  modifications  cancel  each 
other  in  the  total  of  the  world's  income.  But  if  an  income 
is  modified  in  time-shape  through  a  change  in  the  exertions 


194  THE  RATE  OF  INTEREST  [Chap.  IX 

of  laborers,  there  is  no  such  offset,  since  the  total  social 
income  is  actually  modified  also. 

The  labor  of  a  community  is  exerted  in  numerous  ways, 
some  of  which  bring  about  enjoyable  income  quickly,  others 
slowly.  The  labor  of  domestic  servants  is  of  the  former 
variety.  The  cook's  and  waitress's  efforts  result  in  the 
enjoyment  of  food  within  a  day.  Within  almost  as  short 
a  time,  the  chambermaid  and  the  laundress  promote  the 
enjoyment  of  house,  furniture,  and  clothing.  The  baker, 
the  grocer,  the  tailor,  are  but  one  step  behind  the  cook 
and  laimdress;  their  efforts  mature  in  enjoyments  within 
a  few  days  or  weeks.  And  so  we  may  pass  back  to  labor 
increasingly  more  remote  from  enjoyable  income,  until  we 
reach  the  miner  whose  work  comes  to  fruition  years  later, 
or  the  laborer  on  the  Panama  Canal,  whose  work  is  in  the 
service  of  coming  generations. 

The  proportions  in  which  these  various  kinds  of  labor  may 
be  assorted  vary  greatly,  and  it  is  through  this  variation 
that  the  income-stream  of  the  community  changes  its  time- 
shape.  If  there  are  at  any  time  relatively  few  persons  em- 
ployed as  cooks,  bakers,  and  tailors,  and  more  as  builders, 
miners,  and  canal  diggers,  there  will  tend  to  be  less  im- 
mediately enjoyable  income  and  correspondingly  more 
enjoyable  income  several  years  later.  By  withdrawing  labor 
from  one  employment  to  another  it  is  in  the  power  of 
society  to  determine  the  character  of  its  income-stream  not 
only  in  time-shape,  but  also  in  size,  composition,  and  uncer- 
tainty. This  power  is  exerted  through  the  entrepreneur  or 
"enterpriser"  ^  according  to  his  estimate  of  what  return  will 
come  from  each  particular  employment  taken  in  connec- 
tion with  the  sacrifice  involved  and  the  ruling  rate  of 
interest.  Upon  his  judgment  depends  the  future  of  society's 
income,  and  —  since  capital  merely  represents  expected 
income  —  its  future  capital.  If  his  judgment  is  good  and 
he  diverts  labor  from  domestic  service  and  the  production 

*  See  Fetter,   The  Principles  of  Economics,  New  York  (Century), 
1904,  Chap.  XXIX. 


Sec.  10]  CLASSES  OF  OPTIONS  195 

of  commodities  for  immediate  service  to  the  construction 
of  great  engineering  projects  such  as  the  tunnels  to  connect 
Manhattan  Island  with  the  mainland,  he  is  increasing 
future  income  at  the  sacrifice  of  immediate  income,  and 
at  the  same  time  accumulating  capital.  If,  on  the 
contrary,  he  makes  opposite  choice  of  the  employment  of 
labor,  the  opposite  results  will  follow.  Should  his  judg- 
ment be  at  fault  in  either  case,  to  that  extent  will  the 
results  stated  fail  to  be  achieved.  His  task  is  one  of  much 
responsibility  and  great  moment  for  the  weKare  of  the 
world.  The  great  majority  whose  interests  he  sup- 
posedly serves  are  almost  as  much  dependent  on  his  good 
judgment  as  are  the  passengers  in  a  railway  train  de- 
pendent for  their  safety  on  the  good  judgment  of  the 
engineer. 

§10 

Since  the  choice,  for  an  individual,  among  different  options, 
depends  on  the  rate  of  interest  in  the  manner  described 
in  Chapter  VIII,  it  is  clear  that  a  low  rate  favors  the  choice 
of  ascending  income-streams,  but  also  that  the  choice  of 
such  income-streams  reacts  to  raise  the  rate  of  interest. 
If,  on  the  contrary,  the  rate  is  high,  the  opposites  of  both 
these  propositions  hold  true.  Thus,  applying  these  prin- 
ciples to  the  question  of  repairs,  renewals,  and  improve- 
ments, it  is  evident  that  the  lower  the  rate  of  interest,  the 
better  can  the  owner  afford  to  keep  his  carriage  in  repair, 
and  the  higher  the  state  of  efficiency  in  which  it  and  all 
other  instruments  will  be  kept.  But  it  is  equally  clear  that 
the  very  attempt  to  keep  instruments  up  to  the  highest 
level  of  efficiency  tends,  in  turn,  to  increase  the  rate  of  in- 
terest; for  every  repair  means  a  reduction  in  present  in- 
come for  the  sake  of  future  —  a  shifting  forward  in  time 
of  the  income-stream — and  this  will  cause  a  rise  in  the  rate 
of  interest.  Thus,  any  fall  in  the  rate  of  interest,  by  stimu- 
lating repairs,  renewals,  and   betterments,  will   bring  its 


196  THE  RATE  OF   INTEREST  [Chap.  IX 

own  correction  through  oversupplying  future  income  at 
the  expense  of  immediate  income. 

Again,  it  is  evident  that  a  choice  of  the  more  durable 
instruments,  as  compared  with  those  less  durable,  will  be 
favored  by  a  low  rate  of  interest,  and  a  choice  of  short-lived 
instruments  will  be  favored  by  a  high  rate  of  interest. 
If  the  rate  of  interest  should  fall,  there  would  be  a  greater 
tendency  to  build  stone  houses  as  compared  with  wooden. 
The  present  value  of  the  prospective  services  and  disser- 
vices of  stone  houses  as  compared  with  wooden  would  be 
increased;  for  although  stone  houses  are  more  expensive  at 
the  start,  they  endure  longer,  and  their  extra  future  uses, 
which  constitute  their  advantage,  will  have  a  higher  present 
value  if  the  rate  of  interest  is  low  than  if  it  is  high.  We 
find,  therefore,  as  John  Rae  has  so  well  pointed  out,  that 
where  the  rate  of  interest  is  low,  instruments  are  substantial 
and  durable,  and  where  the  rate  of  interest  is  high  they 
are  unsubstantial  and  perishable.  In  this  case,  as  in  the 
preceding  cases,  the  low  rate  of  interest  leads  to  a  choice 
which  shifts  the  income-stream  forward  in  time,  and  thus 
tends  to  raise  the  rate  of  interest,  and  vice  versa. 

In  general,  then,  a  low  rate  favors  the  choice  of  "capital- 
istic" methods  of  production.  The  construction  of  a  sub- 
stantial bridge  which  will  never  wear  out  is  more  likely  to 
pay  if  the  rate  of  interest  is  low  than  if  it  is  high;  for  the 
lower  the  rate  of  interest,  the  higher  will  be  the  present 
value  of  the  remote  income  which  the  permanent  structure 
commands.  Reciprocally,  the  more  "capitalistic"  the 
production,  the  greater  the  tendency  to  raise  the  rate  of 
interest;  so  that  the  existence  of  numerous  options  has  a 
regulative  effect.  Beyond  the  margin  of  choice  there 
always  lie  untouched  options  ready  to  be  exploited  the  in- 
stant the  rate  of  interest  falls.  Among  these,  as  Cassel^  has 
pointed  out,  are  waterworks  of  various  kinds.  Not  only 
the  canals  of  stupendous  size  but  hundreds  of   less  con- 

'  The  Nature  and  Necessity  of  Interest,  London  (Macmillan),  1903, 
p.  122. 


Sec.  10]  CLASSES  OF  OPTIONS  197 

spicuous  waterways  are  subjects  of  possible  investment ; 
among  the  lesser  ones  are  the  Elbe  and  the  Erie  canals; 
and  there  might  be  built  numerous  others  as  soon  as  the 
rate  of  interest  falls  low  enough  to  make  the  return  upon 
cost  equal  to  the  rate  of  interest.  The  same  is  true  of  the 
improving,  dredging,  and  deepening  of  harbors  and  rivers, 
the  use  of  dikes  and  jetties,  and  the  construction  of  irri- 
gation works  for  arid  lands. 

There  is  still  room  for  much  improvement  in  our  railway 
systems  by  making  them  more  efficient  and  more  durable, 
by  making  the  roads  straighter,  the  roadbeds  more 
secure,  the  rolling  stock  heavier,  the  bridges  larger  and 
stronger,  etc.  In  a  new  country  where  the  rate  of  interest 
is  high  and  the  return  on  sacrifice  precarious  or  small,  the 
cheapest  and  most  primitive  form  of  railway  is  first  con- 
structed. Very  often  it  is  a  narrow-gauge  road  with  many 
curves,  costing  little  to  construct,  but  much  to  operate. 
Later,  when  the  rate  of  interest  falls,  or  the  traffic  so  in- 
creases that  the  rate  of  return  on  sacrifice  is  greater,  the 
broad-gauge  comes  into  use  and  the  curves  are  eliminated. 
This  is  the  kind  of  change  which  has  been  proceeding  in 
this  country  with  great  rapidity  during  recent  years. 
There  is  a  transition  from  relatively  small  first  cost  and 
large  running  expenses  to  precisely  the  opposite  type  of 
plant,  in  which  the  cost  is  almost  all  initial  and  the  ex- 
pense of  operation  relatively  insignificant. 


CHAPTER  X 

INVENTION 
§1 

Every  range  of  choice  is  of  necessity  a  range  of  choice 
among  known  options;  consequently  the  range  of  choice 
will  change  as  human  knowledge  is  enlarged  and  increased 
through  invention  and  discovery.  In  the  matter  of  trans- 
portation, man  originally  had  no  choice  but  to  walk. 
Afterward,  when  he  learned  how  to  domesticate  animals, 
the  use  of  horses  for  riding  purposes  opened  a  new  and 
more  rapid  method  of  locomotion.  Still  later,  owing  chiefly 
to  the  invention  of  the  wheel,  the  use  of  vehicles  drawn 
by  horses  was  introduced,  then  the  construction  of  rails 
on  which  vehicles  should  run  brought  a  fourth  method. 
And  now,  with  modern  technical  knowledge,  each  of  the 
foregoing  options  is  split  up  into  a  number  of  subordinate 
options;  there  is  the  possibility  of  street  transit  by  sur- 
face, elevated,  or  subway  transportation,  and  the  surface 
transit  may  be  by  railway,  trolley,  automobile,  vehicles  of 
various  kinds,  bicycle,  or  the  primeval  method  of  walking. 

When  a  new  invention  thus  enlarges  the  range  of  choice, 
the  new  options  introduced  may  be  effectual  or  ineffectual, 
—  generally  the  latter.  The  great  majority  of  patents  do 
not  pay  the  cost  of  procuring  them.  The  reason  for  this 
is  that  when  it  comes  to  exploiting  the  new  option,  the 
rate  of  expected  return  on  cost  is  found  to  be  less  than  the 
rate  of  interest.  Where  the  opposite  is  true  the  invention 
is  effectual,  and  leads  not  only  to  a  change  in  the  range  of 
options,  but  also  to  a  change  in  the  selection  among  them. 

When  inventions  thus  result  in  a  new  option —  in  other 
words,  when  it  is  profitable  to  exploit  them,  — the  effect 

198 


Sec.  2]  INVENTION  199 

necessarily  is,  for  a  time,  to  reduce  the  immediate  income- 
stream  of  the  community,  for  the  sake  of  increasing  the  re- 
moter income-stream.  The  deferred  increase  is  expected 
to  yield  a  return  on  the  immediate  sacrifice  at  a  rate  some- 
times far  greater  than  the  rate  of  interest.  But  this  high 
rate  of  return  on  sacrifice  to  the  exploiter  of  the  newly  dis- 
covered method  of  utilizing  capital  does  not  by  itself  fix 
the  rate  of  interest  at  that  level.  On  the  contrary,  the 
valuation  of  the  property  is  immediately  readjusted  to 
the  new  conditions.  Those  who  are  first  to  enter  the  new 
field,  or,  in  the  slang  of  business,  ''come  in  on  the  ground 
floor,"  will  obtain  a  return  on  their  investment  far  greater 
than  the  rate  of  interest.  But  they  will  immediately  value 
their  property  in  accordance  with  its  expected  productiv- 
ity, and  the  rate  of  interest  on  loan  contracts  will  be  but 
slightly  raised.  The  effect  in  raising  interest  comes  merely 
from  the  shifting  forward  of  the  income-stream,  which 
leaves  the  immediate  income  smaller  than  before,  but 
compensates  for  this  by  a  still  greater  increase  afterwards. 
For,  as  we  have  seen,  when  an  income-stream  is  of  ascend- 
ing type,  the  rate  of  interest,  for  contracts  connecting 
the  periods  of  scarce  income  and  those  of  plentiful  in- 
come, tends  to  be  high. 

§  2 

But,  although  the  effect  of  the  invention  is  to  tilt  social 
income  into  the  ascending  form,  the  individual  who  ex- 
ploits the  process  may,  by  the  methods  of  borrowing  and 
lending  or  buying  and  selling  already  explained,  rectify 
his  distorted  income  curve.  He  may,  if  he  desires,  restore 
his  income  curve  to  the  very  same  time-shape  that  it  had 
before  his  investment  in  the  new  enterprise.  In  this  case 
it  will  be  higher  than  before,  all  along  the  line. 

Thus,  if  his  original  income  curve  were  AB  in  Figure  24, 
and  the  exploitation  of  the  new  invention  required,  for  a 
certain  period,  a  sacrifice  tilting  his  income  curve  to  the 


200 


THE  RATE  OF  INTEREST 


[Chap.  X 


position  of  the  dotted  line  A"CB",  he  might,  by  borrowing, 
obtain  the  income  A'B,'  which  has  the  shape  of  his  original 
income  curve  AB,  but  exceeds  it  all  along  the  line.  Thus, 
the  final  effect  of  the  investment  is  to  enlarge  the  income  of 
the  investor.  Provided  he  can  borrow  against  the  antici- 
pated returns,  not  only  need  he  not  suffer  any  temporary 


Fig.  24. 


reduction  in  income  from  the  necessity  of  investing  in  his 
new  enterprise,  but  he  may  even  be  enabled  to  enjoy  a 
larger  income  from  the  outset. 

But  if  those  who  exploit  the  new  invention  make  little 
or  no  sacrifices  in  their  immediate  income,  others  must; 
and  these  are  they  whose  savings  meet  the  cost  of  exploi- 
tation. Since  the  invention  will  more  than  repay  this  cost 
(whether  or  not  to  those  who  incur  it  does  not  matter), 
the  effect  will  be  to  decrease  immediate  and  increase 
remote  income  for  society  as  a  whole.  Borrowing  and 
lending  merely  distribute  the  pressure  upon  those  most 
willing  to  bear  it ;  but  the  effect  is  necessarily,  for  society, 
to  cause  a  temporary  depression  followed  by  an  ascent  of 
the  income-stream,  and  therefore  to  increase  somewhat  the 


Sec.  3]  INVENTION  201 

rate  of  time-preference  and  the  rate  of  interest.  The  inven- 
tions of  Watt  and  others,  which  led  to  the  present  railway 
system,  are  cases  in  point.  They  caused  the  income-stream 
of  society,  from  being  fairly  uniform,  to  assume  a  rapidly 
ascending  form.  Tlie  earliest  investors  were  compelled 
to  make  great  sacrifices,  and  afterwards,  when  the  fruits 
of  their  labors  began  to  come  in,  they  were  often  foregone 
for  the  sake  of  yet  greater  and  more  remote  returns. 
Throughout  the  period  of  railroad  building,  social  income 
has  been  a  series  of  investment,  return,  and  partial  re- 
investment, and  a  curve  which  would  depict  the  actual 
income  enjoyed  would  show  it  to  be  sharply  ascending. 
Numerous  other  inventions  have  cooperated  to  this  end. 
A  whole  series  of  new  appliances  have  followed  the  dis- 
covery of  electricity.  The  elevator  and  the  steel  skeleton 
have  revolutionized  the  art  of  building. 

In  consequence  of  the  ascending  time-shape  of  the  in- 
come-stream, the  rate  of  interest  has  been  kept  up.  It  is 
not  sufficient,  therefore,  to  say  with  Rae,  that  the  high  rates 
of  return  on  sacrifice  offered  by  the  new  inventions  have 
directly  raised  the  rate  of  interest.  These  very  high  re- 
turns were  secured  only  by  a  few.  They  are  out  of  propor- 
tion to  the  rates  of  interest  ruling  on  loans,  or  the  rates 
of  interest  realized  to  the  ordinary  investor.  These  latter 
are  the  rates  of  interest  in  the  true  sense  of  the  word,  and 
they  were  raised  for  the  ordinary  investor,  because  he  was 
called  to  the  aid  of  those  who  were  in  a  position  to  secure 
the  exceptionally  high  returns,  and  had,  therefore,  tempora- 
rily, to  sacrifice  income.  The  result  is  a  general  rise  in  the 
rate  of  interest,  and  in  consequence  a  revaluation  of  invest- 
ment securities,  and,  in  fact,  of  all  capital.  The  value 
of  capital  sinks  as  the  rate  of  interest  rises,  assuming  that 
the  value  of  the  income  from  the  capital  remains  the  same. 

§  3 
This  revaluation  applies  also  to  the  very  capital  in  which 
the  new  invention  or  discovery  is  embodied.     If  it  is  found 


202  THE  RATE  OF  INTEREST  [Chap.  X 

that  a  million  dollars  invested  in  a  newly  discovered  gold 
mine  will  result  in  a  yield  of  ten  millions  a  year,  that  mine 
will  no  longer  sell  for  its  cost,  but  for  a  sum  far  above  it. 
It  is  the  relation  of  the  income  to  the  new  value  of  the  mine, 
and  not  its  relation  to  the  old  value,  which  will  reflect  the 
true  rate  of  interest.  So,  also,  a  new  machine  may  at  first 
return  an  enormous  rate  of  profit  on  its  cost,  — far  higher 
than  the  rate  of  interest ;  but  soon  the  price  of  the  machine 
in  relation  to  the  value  of  its  services  will  be  adjusted  to  the 
rate  of  interest. 

The  same  principle  holds  of  all  new  enterprises.  The 
original  investors  in  The  Bell  Telephone  Company  realized 
returns  far  beyond  the  interest  on  their  investment;  but 
the  present  investor  pays  a  price  for  Bell  Telephone  stock 
commensurate  with  its  dividends. 

Tlie  effect  of  a  new  invention  on  the  rate  of  interest  is 
therefore  registered,  not  by  the  original  rate  of  return  on 
sacrifice  to  the  lucky  "insiders,"  but  by  the  rate  realized 
to  the  investor  who  comes  in  later  and  invests  at  market 
prices.  These  prices,  in  the  case  of  successful  inventions, 
will  be  far  in  excess  of  the  cost. 

New  devices  will  also  cause  a  revaluation  of  the  older  ones 
which  they  have  displaced,  but  in  this  case  the  new  values 
are  lower  than  before.  Tlie  buzz  saw  rendered  nearly 
valueless  the  mill  plants  equipped  in  the  older  methods, 
and  the  band  saw  had  the  same  effect  with  reference  to  the 
buzz  saw.  Hand  looms  and  presses  became  junk  or  curi- 
osities after  the  advent  of  steam  looms  and  presses,  and 
the  first  forms  of  the  latter  have  in  turn  been  superseded. 
The  reasons  for  these  reductions  in  value  are  simple. 
Each  new  process  produces  a  larger  supply  of  the  particular 
kind  of  service  rendered.  The  price  of  this  service  —e.g. 
sawing  or  printing  —  is  reduced,  and  consequently  the 
capitalized  value  of  the  given  amount  of  such  service  which 
can  be  expected  from  the  older  devices  is  reduced,  and  often 
so  far  reduced  as  to  make  the  reproduction  or  even  the 
repair  of  these  older  instruments  wholly  unprofitable. 


Sec.  4]  INVENTION  203 

§   4 

The  subject  of  the  economic  effect  of  invention,  and  par- 
ticularly of  its  effect  upon  the  rate  of  interest,  has  been 
fully  treated  by  John  Rae,  and  to  him  the  reader  of  this 
book  is  referred  for  extended  study.^  There  is  one  point, 
however,  which  Rae  apparently  did  not  observe,  certainly 
did  not  emphasize,  and  that  is  the  temporary  nature  of  the 
effect  of  invention  in  raising  the  rate  of  interest.  The 
efTect  in  raising  interest  lasts  only  so  long  as  [the  result- 
ing income-stream  is  sufficiently  distorted  in  time-shape 
to  be  of  a  decidedly  ascending  type.  This  period  may  be 
called  the  period  of  investment  or  exploitation,  during  which 
society  is  sacrificing  present  income,  or,  as  it  is  inaccurately 
called,  "investing  capital."  Society,  instead  of  confining 
its  productive  energies  to  the  old  channels  and  obtaining 
a  relatively  immediate  return  in  enjoyable  income,  as  by 
producing  food  products,  clothing,  etc.,  directs  its  labor  to 
great  engineering  enterprises  such  as  constructing  tunnels, 
subways,  water  works,  and  irrigation  systems,  that  is,  to 
instruments  which  cannot  begin  to  contribute  a  return  in 
inenjoyable  income  for  many  years.  In  contemplation, 
future  income,  during  this  period,  is  relatively  plentiful, 
and  in  consequence  of  these  "great  expectations,"  the 
rate  of  interest  will  be  high. 

Later,  however,  there  will  come  a  time  when  the  income- 
stream  ceases  to  ascend,  when  all  the  necessary  investment 
has  been  completed,  when  no  further  exploitation  is  possible, 
and  when  it  is  only  necessary  to  keep  up  the  newly  con- 
structed capital  at  a  constant  level.  When  this  period  is 
reached,  the  after  effect  of  the  invention  will  be  felt. 
Society  will  then  have  a  larger  income-stream  than  before, 
but  no  longer  an  ascending  one.  A  mere  increase  in  the 
size  of  the  income-stream,  while  its  shape  remains  constant, 
has  the  effect,  as  we  have  seen,  not  of  increasing,  but  of 
somewhat  decreasing  the  rate  of  time-preference.      Con- 

'  The  Sociological  Theory  of  Capital. 


204  THE  RATE  OF  INTEREST  [Chap.  X 

sequently  the  after  effect  of  all  inventions  and  discoveries 
is  not  to  increase  but  to  decrease  the  rate  of  interest.  Thus, 
the  railway  inventions  have  led  to  a  half  century  of  invest- 
ment in  railways,  during  which  the  income-stream  of  society 
has  been  constantly  on  the  increase.  To-day,  however, 
the  limit  of  steam  railway  investment  has  been  nearly 
reached  in  some  places,  and  in  others  the  rapidity  of  invest- 
ment is  perceptibly  slackened.  Railroads  have  been  an 
outlet  for  the  investment  of  savings,  and  have  tended  to 
supply  for  them  a  good  return.  As  the  necessity  for  new 
railroads  becomes  less,  this  outlet  diminishes,  and  the 
rate  of  interest  falls. 

But  while  the  after  effect  of  an  old  invention  is  to  reduce 
the  rate  of  interest,  it  may,  of  course,  be  true  that  new  in- 
ventions will  be  made  rapidly  enough  to  neutralize  this 
tendency.  It  is  only  when  there  is  a  cessation  in  the  world's 
output  of  new  inventions  that  the  rate  of  interest  is  thus 
apt  to  fall  back,  but  whenever  invention  is  active  it  rises. 
It  thus  rises  and  falls  according  as  the  introduction  or  the 
exploitation  of  inventions  is  active  or  inactive. 

The  same  principles  apply  not  only  to  invention  in  the 
narrower  mechanical  sense,  but  also  to  scientific  and  geo- 
graphical discoveries.  The  unearthing  of  a  new  bed  of  ore, 
as  in  Cripple  Creek,  Alaska,  or  South  Africa,  has  as  its 
immediate  effect  the  necessity  for  a  considerable  depression 
in  the  immediate  income-stream  of  those  who  desire  to 
exploit  the  new  territory,  but  offers  the  prospect  of  very 
great  increase  in  the  future;  consequently,  the  rate  of  in- 
terest in  such  instances  tends  to  be  very  high.  After  the 
period  of  exploitation,  however,  the  income  curve  ceases 
to  rise  and  begins  to  fall.  Thereupon  the  rate  of  preference 
for  present  over  future  income  assumes  the  opposite  ten- 
dency, and  the  rate  of  interest  declines. 

§5 

It  has  not  been  the  purpose  of  this  chapter  to  investigate 
the  general  effect  of  inventions,  but  merely  their  effect  on 


Sec.  5]  INVENTION  205 

the  rate  of  interest.  Before  leaving  the  subject,  however, 
it  should  at  least  be  stated  that  invention  is  the  basis  of 
progress  in  civilization.  The  inventions  of  fire,  the  alpha- 
bet, and  the  means  of  utihzing  power — first  of  animals, 
then  of  wind  and  water,  then  of  steam  and  electricity  — 
and  their  manifold  applications,  especially  to  transportation 
and  communication,  have  made  it  possible  for  the  earth 
to  support  its  increasing  population,  and  deferred  the 
Malthusian  pressure  upon  the  means  of  subsistence;  they 
have  made  possible  the  stable  existence  of  great  political 
units  such  as  the  United  States;  and  they  have  given  op- 
portunity for  the  presentation,  diffusion,  and  increase  of 
knowledge  in  all  its  forms  of  art,  literature,  and  science. 
And  thus  it  happens  that  invention  is  self-perpetuating. 
For  not  only  has  science  sprung  from  inventions  such  as  the 
printing  press,  the  telegraph,  and  specific  scientific  instru- 
ments for  observation,  like  microscopes  and  telescopes,  or 
for  measurements,  like  chronographs,  balances,  and  microme- 
ters; but  modern  science  is  now  in  turn  yielding  new 
inventions.  Helmholz's  researches  in  sound  led  to  the 
telephone;  Maxwell's  and  Hertz's  researches  on  ethereal 
waves  led  to  wireless  telegraphy.  Nations  like  the  United 
States  and  Germany  will  lead  in  civilization  by  taking  the 
greatest  advantage  of  this  self-propagating  principle  of 
invention;  and  nations  like  China,  which  give  it  the  least 
attention,  will  lag  behind. 

The  conditions  for  the  most  rapid  multiplication  of  in- 
ventions are :  (1)  personal  efficiency,  dependent  on  breeding, 
hygienic  habits,  and  the  education  (both  general  and  tech- 
nical) of  the  faculties;  and  for  this  the  Greek  motto  "a 
sane  mind  in  a  sane  body"  is  in  point;  wherefore  Gal  ton 
seems  to  show  that  in  Greece  genius  was  far  more  com- 
mon than  in  modern  civilization;  (2)  the  ease  of  diffusion 
of  knowledge ;  (3)  the  size  of  the  population  within  which 
the  diffusion  occurs,  — the  larger  the  population  the  greater 
being  the  number  of  inventive  geniuses,  the  greater  their 
incentive,  and  the  wider  their  sphere  of  influence;    (4)  the 


206  THE  RATE  OF  INTEREST  [Chap.  X 

encouragement  of  invention  through  patent  protection, 
and  more  especially  through  the  early  discovery  and  ap- 
proval of  genius.  Inventors  are  at  once  the  rarest  and 
most  precious  flower  of  the  country.  Too  often  they  are 
crushed  by  the  obstacles  of  poverty,  prejudice,  or  ridicule. 
While  this  is  less  so  to-day  than  in  the  days  of  Roger  Bacon 
or  Galileo,  it  still  requires  far  too  much  time  for  the  Edisons 
or  the  Burbanks  to  get  their  start.  The  decades  in  which 
these  rare  brains  are  doing  their  wonderful  work  are  at 
most  few,  and  it  is  worth  many  millions  of  money  for  their 
countrymen  to  set  them  to  work  early.  As  Huxley  says, 
it  should  be  the  business  of  any  educational  system  to 
seek  out  the  genius  and  train  him  for  the  service  of  his 
fellows;  for  whether  he  will  or  not,  the  inventor  cannot 
keep  the  benefits  of  his  invention  to  himself.  In  fact,  it  is 
seldom  that  he  can  get  even  a  small  share  of  the  benefits. 
The  citizens  of  the  world  at  large  are  the  beneficiaries, 
and  being  themselves  not  sufficiently  clever  to  invent, 
they  should  at  least  be  sufficiently  alive  to  their  own  in- 
terest to  subsidize  the  one  man  in  a  million  who  can. 


CHAPTER  XI 

THIRD     APPROXIMATION     TO     THE     THEORY    OF     INTEREST 
(assuming  INCOME   UNCERTAIN) 

§   1 

Up  to  this  point  we  have  ignored  the  element  of  chance, 
by  assuming  that  the  entire  futm-e  income-stream,  or  at 
any  rate,  such  portions  of  it  as  need  to  influence  present 
choice,  are  foreknown  and  mapped  out  in  advance.  In 
the  preceding  chapter,  we  have  assumed  inventions  to  be 
surprises, —  sudden  enlargements  of  knowledge  coming 
upon  us  without  previous  anticipation.  In  other  words, 
we  have  assumed  that  men  disregard  future  inventions 
and  act  as  though  their  knowledge  of  the  future  were  per- 
fect. This  assumption,  hke  the  assumption  that  bodies 
fall  in  vacuo,  in  the  ordinary  presentation  of  the  theory 
of  gravitation,  has  enabled  us  to  complete  our  formal 
statement  of  the  theory  more  easily,  although  at  the 
expense  of  exact  conformity  to  actual  historical  fact ;  for, 
in  the  concrete  world,  the  most  conspicuous  characteristic 
of  the  future  is  its  uncertainty.  Consequently  the  intro- 
duction of  the  element  of  risk  will  give,  as  by  magic,  the 
aspect  of  reahty.  The  general  principles  which  have 
been  stated,  however,  will  still  hold  true  when  we  assume 
uncertainty  instead  of  certainty;  they  merely  require 
to  be  supplemented  by  other  principles. 

One  consequence  of  changing  our  assumption  as  to  the 
certainty  of  future  events  is  to  compel  the  abandonment  of 
the  idea  of  a  single  rate  of  interest.  Instead  of  a  single 
rate  of  interest  representing  the  rate  of  exchange  between 
this  year  and  next  year,  we  now  find  a  great  variety  of  rates 
according  to  the  risk  involved.     The  rate  in  every  loan 

207 


208  THE  RATE  OF  INTEREST  [Chap.  XI 

contract  is  adjusted  on  the  basis  of  the  degree  of  security 
given.  Thus,  security  may  be  furnished  by  simple  indorse- 
ment of  reputable  persons,  in  which  case  the  degree  of  se- 
curity will  be  the  greater  the  larger  the  number  of 
indorsers  and  the  higher  the  credit  which  they  possess; 
or  it  may  be  by  the  deposit  of  collateral  securities.  The 
necessity  of  the  latter  operation  will  affect  a  man's  ability 
to  borrow,  and  limit  the  extent  to  which  he  may  modify 
his  income-stream  by  this  means.  It  will  not  be  possible, 
as  hitherto  assumed,  for  a  man  to  modify  his  income-stream 
at  will,  but  only  up  to  the  limit  of  his  credit.  In  conse- 
quence of  this  limitation  upon  his  borrowing  power,  he  may 
not  succeed  in  modifying  his  income-stream  sufficiently  to 
bring  the  rate  of  preference  between  present  and  future 
income  down  to  the  rate  of  interest  ruling  in  the  mar- 
ket ;  and  for  like  reasons,  he  may  not  succeed  in  bringing 
the  rate  of  return  on  sacrifice  into  conformity  with  the 
rate  of  interest. 

One  feature  of  this  limitation  is  the  fact  that  the  abihty 
to  borrow  depends,  not  so  much  on  the  amount  of  capital 
which  the  would-be  borrower  possesses,  as  on  the  form  in 
which  that  capital  happens  to  be.  Some  securities  are 
readily  accepted  as  collateral,  and  accepted  for  a  high  per- 
centage of  their  face  value,  whereas  others  will  pass  with 
difficulty  and  only  for  a  low  percentage.  The  recent  ten- 
dency to  change  the  organization  of  business  to  the  corpo- 
rate form  has  had  a  striking  effect  in  increasing  the  power 
to  borrow.  Whereas  formerly  many  businesses  were  con- 
ducted as  partnerships  and  on  a  small  scale,  numerous 
stocks  and  bonds  have  now  been  substituted  for  the  old 
rights  of  partnership  and  other  less  negotiable  forms  of 
security ;  hence  the  possessors  of  these  securities  have  wider 
opportunities  to  deposit  collateral,  and  the  tendency  to 
borrow  has  received  a  decided  impulse.  This  explains  to  a 
large  extent  the  investing  and  speculative  mania  which 
followed  the  recent  widespread  consolidation  and  formation 
of  trusts. 


Sec.  1]  THIRD  APPROXIMATION  209 

Where  the  security  does  not  exist  in  the  convenient  form 
of  written  certificates,  there  is  often  considerable  difficulty 
in  negotiating  a  loan.  If  commodities  are  used  for  security, 
they  must  ordinarily  be  themselves  deposited  with  the 
lender,  —  in  other  words,  put  in  pawn.  Where  the  bor- 
rowing takes  place  in  pawn  shops,  it  is  not  because  of  the 
inadequacy  of  the  security,  but  because  of  its  inconvenient 
form,  that  the  rate  of  interest  is  usually  very  high.  The 
pawnbroker  will  need  to  charge  a  high  rate  of  interest, 
partly  because  he  needs  storage  room  for  the  security  he 
accepts,  partly  because  he  needs  special  clerks  and  experts 
to  appraise  the  articles  deposited,  and  partly  because,  in 
many  cases,  he  needs  to  find  a  market  in  which  to  sell  them 
when  not  redeemed.  He  is,  moreover,  able  to  secure  these 
high  rates  partly  because  pawnbroking  is  in  bad  odor,  and 
those  who  go  into  it  therefore  find  a  relative  monopoly; 
and  partly  because  of  the  fact  that  the  customers  usually 
have,  either  from  poverty  or  personal  peculiarity,  a  rela- 
tively high  valuation  of  present  over  future  income.  The 
effect  of  their  flocking  to  the  pawn  shop  is  to  reduce  this 
high  valuation;  but  it  will  not  reduce  it  to  the  general 
level  in  the  community,  because  these  persons  do  not  have 
access  to  the  loan  market  in  which  the  ordinary  business 
man  deals.  To  them,  imdoubtedly,  the  fact  that  they 
cannot  borrow  except  at  high  or  usurious  rates  is  often  a 
great  hardship;  but  it  has,  as  one  beneficent  effect,  the 
discouragement  of  getting  unwisely  into  debt.  Those  who 
patronize  pawn  shops  to  a  large  extent  do  so  because 
they  possess  little  foresight  and  self-control,  and  the  im- 
pediment which  they  find  in  the  shape  of  a  high  interest  rate 
in  a  measure  takes  the  place  of  the  self-control  and  foresight 
which  they  should  possess.  Were  it  possible  for  this  class 
to  borrow  at  lower  rates,  many  of  them  would  sink  even 
more  deeply  into  debt  than  they  actually  do.  Thus,  if 
slavery  were  legalized  and  it  were  possible  for  a  man  to 
mortgage  the  income  from  his  own  labor,  it  is  unfortu- 
nately true  that  many  would  avail  themselves  of  this  privi- 


210  THE  RATE  OF  INTEREST  [Chap.  XI 

lege,  and  would  drop  to  the  lowest  place  in  the  economic 
scale, —  slavery.  The  fact  that  such  contracts  are  illegal 
fixes  a  limit  below  which  the  ordinary  ne'er-do-weel  can- 
not fall.  At  this  point  his  rate  of  preference  for  present 
over  future  is  not  in  harmony  with  the  rate  of  interest  in 
the  community.  When  the  market  rate  of  interest  is  5  per 
cent.,  he  may  feel  a  rate  of  preference  of  25  per  cent. 

§  2 

We  find,  therefore,  that  the  introduction  of  the  element 
of  chance,  and  the  necessity  of  overcoming  it  by  the  giving 
of  security,  has  as  one  of  its  effects  the  splitting  up  of  the 
market  into  a  number  of  sub-markets.  Instead  of  one  huge 
market  in  which  there  is  a  single  rate  of  interest,  to  which 
every  individual  conforms  his  own  rate  of  preference,  we  now 
find  a  number  of  separate  markets,  a  number  of  different 
rates  of  interest,  and  a  very  imperfect  adjustment  of  the 
individual  rates  of  preference  to  those  rates. 

We  need  here  to  emphasize  the  distinction  between  a 
commercial  rate  of  interest  which  includes  risk  and  a  pure 
or  riskless  rate  of  interest.^  The  commercial  rates  vary 
widely,  although  the  range  of  variation  for  rates  on  loans 
easily  negotiable  is  relatively  small.  In  ordinary  real  estate 
mortgages  in  the  same  market  the  range  of  variation  is 
seldom  over  1  per  cent. 

If  we  pass  from  explicit  interest,  or  the  rate  of  interest 
involved  in  a  loan  contract,  to  implicit  interest  or  the  rate 
involved  in  purchases  and  sales  of  property  of  various  kinds, 
we  see  again  that  the  greater  the  risk  the  higher  the  "  basis" 
on  which  a  security  will  sell.  A  "gilt-edge"  security  may 
seU  on  a  3  per  cent,  basis,  when  a  less  known  or  less  salable 
security  will  be  selling  on  a  6  per  cent,  basis.  The  element 
of  risk  will  affect  also  the  value  of  the  collateral  securities. 
Their  availability  for  this  purpose  will  increase  their  sala- 

'  See  Glossary  under  "Basis" ;  also  The  Nature  of  Capital  and  Income, 
Chap.  XVI. 


Sec.  3]  THIRD  APPROXIMATION  211 

bility  and  enchance  their  price.  On  the  other  hand,  when,  as 
in  times  of  crises,  the  collateral  is  imperatively  demanded,  it 
often  happens  that,  for  purposes  of  liquidation,  it  is  sold 
at  a  sacrifice. 

In  the  same  way  that  risk  causes  the  rates  of  explicit 
interest  in  a  community  to  diverge  from  each  other,  or 
causes  rates  of  preference  to  separate  from  rates  of  interest, 
it  will  cause  the  rates  of  implicit  interest  to  diverge.  The 
same  individual  who  would  borrow,  if  he  could,  at  25  per 
cent.,  but  who  lacks  the  necessary  security,  must  devote 
his  energies  instead  to  acquiring  or  producing  instru- 
ments which  will  have  a  return  on  sacrifice  at  the  25 
per  cent,  level.  Although  it  would  be  more  economical, 
if  he  could  only  borrow  the  money,  to  build  durable  houses, 
he  will  build  inferior  ones.  Hence  the  anomaly,  that  even 
in  countries  where  the  rate  of  interest  is  low,  there  will  be 
primitive  communities  in  which  the  instruments  possessed, 
in  the  form  of  dwellings,  tools,  implements,  etc.,  are  far 
less  substantial  than  is  compatible  with  the  low  rate  of 
interest. 

§3 

Among  other  phenomena  which  follow  from  the  existence 
of  risk  are  the  variations  in  the  duration  of  loans.  Where 
the  future  is  regarded  as  safe,  loan  contracts  tend  to  be 
longer  in  time  than  otherwise.  Railway  and  government 
securities  are  thus  often  drawn  for  haK  a  century  or  more. 
On  the  other  hand,  to  provide  for  the  uncertainty  of  the 
immediate  future,  the  "call  loan"  is  devised.  This  is  a 
loan  which  has  no  specified  due  date,  but  can  be  demanded 
at  the  option  of  the  lender  whenever  some  circumstance 
makes  this  course  advisable.  A  loan  contract  of  this  kind 
brings  the  burden  of  risk  on  the  borrower  and  relatively 
relieves  the  lender,  and  in  consequence,  under  such  con- 
ditions, the  rate  on  call  loans  will  usually  tend  to  be  low. 

The  same  principles  will  explain  the  low  rate  of  implicit 
interest  in  many  cases.    Where  a  security,  because  it  is  well 


212  THE  RATE  OF  INTEREST  [Chap.  XI 

known,  or  for  any  other  reason,  has  a  high  degree  of  sala- 
bility,  that  is,  can  be  sold  on  short  notice  without  great 
sacrifice,  the  price  will  be  higher  than  otherwise,  and  the 
rate  of  interest  it  yields  will  therefore  be  low.  Hence  it  is 
that  the  rate  of  interest  on  individual  mortgages  will  be 
higher  than  the  rate  of  interest  on  more  marketable  se- 
cm'ities.  It  is  usually  considered  an  advantage  to  any 
stock  to  be  listed  on  the  stock  exchange;  for,  being  thus 
widely  known,  should  the  necessity  arise  to  sell  it,  there  will 
be  found  a  more  ready  market. 

The  most  salable  of  all  properties  is,  of  course,  money; 
and  as  Karl  Menger  has  pointed  out,  it  is  precisely  this 
salability  which  makes  it  money.  The  convenience  of  being 
able,  without  any  previous  preparation,  to  dispose  of  it 
for  any  exchange,  is  itself  a  sufficient  return  upon  the  capital 
which  a  man  keeps  in  this  form,  and  takes  the  place  of  any 
rate  of  interest  in  the  ordinary  sense  of  a  money  payment. 

§4 

A  further  conssequence  of  the  introduction  of  the  element 
of  risk  is  the  wide  divergence  between  the  actual  rate  of 
return  realized  by  an  investor  and  the  expected  rate.  When 
risk  was  regarded  as  absent,  it  was  assumed  that  the  ex- 
pected always  happened;  but  in  the  actual  world  this  is 
far  from  true.  Those  who  invested  in  some  of  the  mining 
"bonanzas"  many  years  ago  have  received  a  rate  of  return 
of  many  hundred  per  cent. ;  and  far  in  excess  of  the  rate  of 
interest  which  they  would  have  been  willing  to  take  for  a 
loan.  Reversely,  those  who  invested  in  the  South  Sea 
Bubble  found  an  opposite  disparity  between  their  expecta- 
tions and  their  realizations.  Risk  is  especially  conspicu- 
ous at  the  time  of  new  inventions  or  discoveries.  Almost 
all  prediction  is  based  on  a  belief  in  the  repetition  of  past 
experience;  but  at  these  times,  past  experience  is  a  poor 
guide.  When  new  inventions  are  made,  uncertainty 
is  introduced,  speculation  follows,  and  after  that,  great 


Sec.  5]  THIRD  APPROXIMATION  213 

wealth  or  ruin.  The  history  of  gold  and  silver  discoveries 
and  of  the  invention  of  rubber,  steel,  and  electrical  appli- 
ances, is  filled  with  tales  of  thousands  of  wrecked  fortunes, 
by  the  side  of  which  tower  the  fortunes  of  to-day's  nou- 
veaux  riches. 

The  rate  of  interest  is  always  based  upon  expectation, 
however  little  this  may  be  justified  by  realization.  Man 
makes  his  guess  of  the  future  and  stakes  his  action  upon  it. 
In  his  guess  he  discounts  everything  he  can  foresee  or 
estimate,  even  future  inventions  and  their  effects.  In  a 
recent  estimate  of  the  value  of  a  copper  mine,  allowance  was 
made  for  future  economies  from  inventions  which  might 
reasonably  be  expected.  So,  also,  the  buyer  of  machinery 
allows  not  simply  for  its  depreciation  through  physical 
wear,  but  for  its  being  possibly  superseded.  New  invest- 
ments in  steam  railroads  are  to-day  made  with  due  regard 
to  the  possibility  that  the  road  may  within  a  few  years  be 
run  by  electricity.  It  may  easily  happen  that  in  a  coun- 
try consisting  of  oversanguine  persons,  or  during  a  period 
when  business  men  are  overhopeful,  the  rate  of  interest 
will  be  higher  than  the  event  justifies.  It  is  probable 
that,  in  ordinary  communities,  realization  justifies  the 
average  expectation;  but  in  the  individual  case  this  is 
not  always  true,  otherwise  there  would  be  no  risk.  Risk 
is  due  to  partial  knowledge.  Our  present  acts  must  be 
controlled  by  the  future,  not  as  it  actually  is,  but  as  it 
looks  to  us  through  the  veil  of  chance. 

§5 

In  the  preceding  section  we  discussed  the  effect  of 
risk  on  the  pseudo-  or  impure  rate  of  interest ;  ^  that  is, 
the  rate  on  unsafe  investments.  But  even  the  pure  rate 
of  interest,  or  the  rate  on  safe  investments,  is  affected 
by  risk.  The  effect  is  different  according  to  the  various 
conditions  which  may  influence  the  rate  of  preference  for 

*  See  The  Nature  of  Capital  and  Income,  Chap.  XVI,  §  8. 


214  THE  RATE  OF  INTEREST  [Chap.  XI 

present  over  future  income.  Where  the  risk  relates  to 
human  life,  the  rate  of  preference  for  present  over  future 
income  is  increased.^  Consequently  the  rate  of  interest, 
even  on  safe  loans,  will  be  raised  by  the  existence  of 
such  risk.  The  man  who  looks  forward  to  a  short  or 
precarious  existence  will  be  less  likely  to  make  permanent 
investments,  or,  if  he  makes  them,  less  Ukely  to  pay  a  high 
price  for  them.  Only  a  low  price,  that  is,  a  high  rate  of 
interest,  will  induce  him  to  invest.  When  the  risk  relates, 
however,  not  to  the  duration  of  life,  but  to  the  income- 
stream,  the  effect  upon  the  rate  of  interest  will  depend 
upon  which  portion  of  the  income-stream  is  subject  to 
risk.  If  the  immediately  ensuing  income  is  insecure, 
whereas  the  remoter  income  is  sure,  the  rate  of  preference 
for  immediate  as  compared  with  remote  income  will,  as  was 
shown,  be  high,  and  consequently  the  effect  of  such  a  risk 
upon  the  rate  of  interest  will  be  to  raise  it.  But  if,  as  is 
ordinarily  the  case,  the  risk  applies  more  especially  to  the 
remoter  income  than  to  immediate,  the  effect  is  the  exact 
opposite ;  namely,  to  lower  the  rate  of  interest  on  a  safe 
loan.  This  is,  perhaps,  the  typical  case.  If  a  man  regards 
the  income  for  the  next  few  years  as  sure,  but  is  in  doubt  as 
to  its  continuance  into  the  remoter  future,  he  will  be  more 
keenly  alive  to  the  needs  of  that  future,  and  will  consequently 
have  a  less  keen  preference  for  the  present.  He  will  then 
be  willing,  even  at  a  very  low  rate  of  interest,  to  invest,  out 
of  his  present  assured  income,  something  to  eke  out  the  less 
sure  income  of  the  future.  The  effect  of  risk  in  this  case, 
therefore,  is  to  lower  the  rate  of  interest  on  safe  loans, 
though  at  the  same  time,  as  already  explained,  it  will  raise 
the  rate  of  interest  on  unsafe  loans.  Consequently,  in  times 
of  great  social  unrest  and  danger,  we  witness  the  anomalous 
combination  of  high  rates  where  inadequate  security  is 
given,  coexistent  with  low  rates  on  investments  regarded 
as  perfectly  safe.  In  commercial  language,  when  an 
investor  cannot  find  many  investments  into  which  he  may 

'  Cf.  Carver's  The  Distribution  of  Wealth,  p.  256. 


Sec.  6]  THIRD  APPROXIMATION  215 

put  his  money  without  risk  of  losing  it,  he  will  pay  a 
high  price  for  the  few  which  are  open  to  him.  It  has  been 
noted  in  times  of  revolution  that  some  capitalists  have 
preferred  to  forego  the  chance  of  all  interest  and  merely 
hoard  their  capital  in  money  form,  even  paying  for  storage 
charges,  which  amounts  to  a  negative  rate  of  interest. 

§  6 

When  risk  thus  operates  to  lower  the  rate  of  interest 
on  safe  investments  and  to  raise  the  rate  on  unsafe  in- 
vestments, there  immediately  arises  a  tendency  to  dif- 
ferentiate two  classes  of  securities  and  two  classes  of 
investors,  —  precarious  securities  and  adventurous  invest- 
ors on  the  one  hand,  and  safe  securities  and  conservative 
investors  on  the  other.  Risk  is  inevitable  in  every  business, 
but  is  regarded  by  most  people  as  a  burden ;  hence  the  few 
who  are  able  and  willing  to  assume  this  burden  become 
a  separate  class.  To-day,  when  any  enterprise  is  organized 
in  corporate  form,  it  is  usual  to  recognize  this  tendency  by 
dividing  the  securities  into  stocks  and  bonds,  the  stock- 
holder being  the  person  who  assumes  the  risk  and,  theoreti- 
cally at  least,  guarantees  that  the  bondholder  shall  be  free 
of  all  risk,  A\Tiich  persons  shall  fall  into  the  class  of  risk 
takers  and  which  not,  is  determined  by  their  relative 
coefficients  of  caution,^  as  well  as  by  the  relative  degree  of 
risk  which  an  enterprise  would  involve  for  the  various  in- 
dividuals. Tlie  same  enterprise  may  be  perilous  to  one 
and  comparatively  safe  to  another,  because  of  superior 
knowledge  or  other  conditions;  and  the  same  degree  of 
risk  may  repel  one  individual  more  than  another,  owing 
to  differences  in  temperament,  or,  most  important  of  all, 
differences  in  amount  of  capital.^ 

This  shifting  of  risk  from  those  on  whom  it  bears  heavily 
to  those  who  can  best  assume  it,  discloses  another  motive 

'  See  The  Nature  of  Capital  and  Income,  Chap.  XVI,  §  6. 
2  Ibid.,  Appendix  to  Chap.  XVI,  p.  409. 


216  THE  RATE  OF  INTEREST  [Chap.  XI 

for  borrowing  and  lending  besides  those  which  were  discussed 
in  a  previous  chapter.  Lending,  in  modern  finance,  often 
indicates  not  simply  a  difference  in  time-shape  as  between 
two  income-streams,  but  also  a  difference  of  risk.  The  object 
of  lending  which  was  emphasized  in  earlier  chapters,  before 
the  risk  element  was  introduced  into  the  discussion,  was 
to  alter  the  time-shape  of  the  income-stream,  the  borrower 
desiring  to  increase  his  present  income  and  decrease  his 
future,  and  the  lender  desiring,  on  the  contrary,  to  decrease 
his  present  income  and  add  to  his  future.  But  the  stock- 
holder and  bondholder  do  not  differ  in  this  way  so  much 
as  in  respect  to  risk.  They  are  both  investors,  and 
stand  in  a  very  similar  position  as  to  the  effect  of  their 
investment  on  the  time-shape  of  their  income.  For  the 
stockholder,  however,  there  is  a  risk  attached  to  his  income- 
stream  from  which  the  bondholder  is  relatively  free.  It 
is  this  difference  in  risk  which  is  the  primary  reason  for 
the  distinction  between  stockholders  and  bondholders. 
The  bondholder  "commutes"  ^  his  chance  of  a  high  income 
for  the  certainty  of  a  steady  income. 

The  existence  of  this  risk,  tending,  as  we  have  seen,  to 
raise  the  rate  of  impure  interest  and  lower  that  of  pure 
interest,  has  as  its  effect  the  lowering  of  the  price  of  stocks 
and  the  raising  of  the  price  of  bonds  from  what  would  have 
been  their  respective  prices  had  the  risk  in  question  been 
absent.  On  the  other  hand,  the  separation  of  the  investors 
into  stockholders  and  bondholders  reacts  upon  the  prices 
of  stocks  and  bonds  and  tends  to  lessen  the  disparity 
between  them.  Were  there  no  bonds,  but  only  stocks,  the 
price  of  the  stock  would  have  to  be  lower  than  it  now  is, 
in  order  to  induce  the  timid  investor  to  buy.  In  other 
words,  the  effect  of  the  separation  between  risky  and  safe 
investments  is  at  once  to  moderate  the  lowness  of  the  low 

*  Cf.  Hadley,  Economics,  p.  270.  The  rate  of  interest,  however, 
is  not,  properly  speaking,  the  rate  of  coiximutation ;  for  the  rate  of 
commutation  would  be  the  ratio  between  the  average  earnings  of  the 
stockholder  and  the  average  earnings  of  the  bondholder,  whereas 
the  rate  of  interest  is  the  ratio  between  income  and  capital. 


Sec.  7]  THIRD   APPROXIMATION  217 

rate  on  safe  investments  and  the  height  of  the  high  rate 
on  the  unsafe  investments. 

The  same  tendency,  to  reduce  the  disparity  between  the 
rates  of  interest  on  safe  and  unsafe  investments,  grows  out 
of  the  practice  of  insurance.  One  effect  of  insurance  ^  is 
to  raise  the  value  of  capital  subject  to  risk  of  fire  or  other  in- 
surable risks,  by  consohdating  those  risks  and  thus  virtually 
reducing  them.  But  this  rise  in  the  value  of  capital  implies 
a  reduction  in  the  rate  of  interest  which  it  yields.  Again, 
the  effect  of  speculation,  by  setting  aside  a  certain  class 
of  persons  to  assume  the  risks  of  trade,  has  the  effect  of 
reducing  these  risks  by  putting  them  in  the  hands  of  those 
who  have  most  knowledge;  for,  as  we  have  seen,  risk  varies 
inversely  with  knowledge.  In  this  way  the  whole  plane 
of  business  is  put  more  nearly  on  a  uniform  basis  so  far  as 
the  rate  of  interest  is  concerned. 

§  7 

We  see,  then,  that  the  element  of  risk  introduces  dis- 
turbances into  those  determining  conditions  which  were 
expressed  in  previous  chapters  as  explaining  the  rate  of 
interest.  To  summarize  these  disturbances,  we  may  apply 
the  risk  factor  to  each  of  the  six  conditions  which  were 
originally  stated  as  determining  interest.  We  shall  find  that 
its  effects  are  as  follows :  — 

1.  The  condition  that  each  individual  has  a  given  range 
of  choice  still  holds  true,  but  these  choices  are  no  longer 
confined  to  absolutely  certain  optional  income-streams, 
but  include  options  with  risk.  That  is,  each  individual 
finds  open  to  his  choice  a  given  set  of  options  which 
differ  in  size,  time-shape,  composition,  and  risk. 

2.  Rates  of  preference  for  present  over  future  goods  are 
of  two  kinds,  according  as  the  goods  are  comparatively  cer- 
tain or  uncertain.  The  marginal  rate  of  preference  for  a 
certain  present  over  a  certain  future  good,  or  the  pure  rate 

*  See  The  Nature  of  Capital  and  Income,  Chap.  XVI. 


218  THE  RATE  OF  INTEREST  [Chap.  XI 

of  time-preference,  depends  upon  the  character  of  the 
total  income-stream,  —  not  only  its  size,  shape,  and  com- 
position, but  also  and  particularly  upon  the  degree  of  cer- 
tainty attaching  to  various  parts  of  it  and  the  degree 
of  certainty  of  life  of  the  recipient.  Again,  the  preference 
rate  for  present  certain  income  as  compared  with  future  un- 
certain income,  or  the  impure  rate  of  time-preference, 
will,  in  normal  individuals,  be  greater  than  if  both  in- 
comes were  certain,  and  will  be  the  greater,  the  higher  the 
risk  and  the  higher  the  caution  in  assuming  it. 

3.  Pure  rates  of  time- preference  (as  among  certain  goods) 
in  different  individuals  tend  toward  equality  by  the  prac- 
tice of  borrowing  and  lending,  and  more  generally,  buying 
and  selling;  but  this  equality  is  not  in  all  cases  attain- 
able, because  of  limitations  on  the  freedom  to  modify 
the  income-stream  at  will.  These  limitations  grow  out 
of  the  existence  of  the  element  of  risk.  There  are  various 
means  of  reducing  or  avoiding  risk, — in  particular,  by 
the  devices  of  collateral  security,  indorsement,  under- 
writing, etc.,  but  all  of  these  processes  have  more  or  less 
definite  limitations.  In  consequence,  it  is  not  always 
possible  to  provide  security  for  as  large  a  loan  as  would 
be  necessary  to  change  the  income-stream  enough  to  reduce 
the  rate  of  preference  of  the  borrower  to  the  rate  of 
interest.  If  the  security  is  adequate,  the  rate  of  preference 
will  be  equalized  with  the  rate  of  interest;  if  not,  it  will 
remain  above  it.  Where  the  security  introduces  impedi- 
ments which  affect  the  lender  as  well  as  the  borrower,  it 
will  also  happen  that  the  rate  of  interest  will  be  raised,  as 
in  the  case  of  pawn  shops  which  hold  in  pledge  their  motley 
assortment  of  cumbersome  merchandise.  Thus,  instead 
of  one  rate  for  several  loans,  there  will  be  a  number  of 
separate  rates  and  a  number  of  separate  markets,  accord- 
ing to  the  nature  of  the  security  asked  and  given. 

At  the  same  time  there  will  be  a  tendency  to  ask  and 
receive  loans  with  inadequate  security.  This  introduces 
a  pseudo-  or  impure  rate  of  interest  which  wiU  be  above 


Sec.  7]  THIRD  APPROXIMATION  219 

the  pure  rate  by  a  margin  differing  according  to  risk  and 
caution. 

4.  When  risk  was  left  out  of  account,  it  was  stated  that 
from  among  a  number  of  different  alternatives  the  indi- 
vidual would  select  that  one  which  had  the  maximum  pres- 
ent value,  —  in  other  words,  that  one  which,  compared  with 
its  nearest  neighbors,  possessed  a  rate  of  return  on  sacrifice 
equal  to  the  rate  of  preference,  and  therefore  to  the  rate 
of  interest.  When  the  risk  element  is  introduced,  it  will 
still  be  true  that  the  maximum  present  value  is  selected; 
but  in  translating  future  uncertain  income  to  present 
cash  value,  use  must  now  be  made  of  the  probability  and 
caution  factors.  One  consequence  is  that  when  we  express 
this  principle  of  maximum  present  value  in  its  alternative 
form  in  terms  of  the  "marginal  rate  of  return  on  sacrifice," 
we  must  qualify  this  expression  as  the  "marginal  rate  of 
anticipated  return  on  sacrifice."  The  rate  of  return  on 
sacrifice  which  will  be  actually  realized  may  turn  out  to 
be  widely  different  from  that  originally  anticipated. 

5.  In  the  former  approximations,  where  the  element  of 
risk  was  considered  absent,  it  was  shown  that  the  aggre- 
gate modification  of  the  income-streams  of  individuals  for 
every  period  of  time  was  zero.  What  was  borrowed  equaled 
what  was  lent,  or  what  was  added  by  sale  was  equal  to 
what  was  subtracted  by  purchase.  The  same  principle 
still  applies;  for  what  one  person  pays,  another  person 
must  receive. 

6.  In  the  former  approximations,  the  total  present  value 
of  the  projected  modifications  of  one's  income-stream  was 
zero;  that  is,  the  present  value  of  the  loans  equaled  the 
present  value  of  the  borrowings;  or  the  present  value  of 
the  additions  and  subtractions  due  to  buying  and  selling 
balanced  each  other.  In  our  present  discaission,  in  which 
future  income  is  recognized  as  uncertain,  this  principle  still 
holds  true,  but  only  in  the  sense  that  the  present  market 
values  balance  at  the  moment  when  the  future  loans  or 
other  modifications  are  planned  and  decided  upon.     The 


220  THE  RATE  OF  INTEREST  [Chap.  XI 

fact  that  risk  is  present  may  lead  to  a  wide  discrepancy 
between  the  original  expectation  and  the  actual  realiza- 
tion. In  liquidation  there  may  be  default  or  bankruptcy. 
When  the  case  is  not  one  of  a  loan  contract,  but  relates 
merely  to  the  difference  in  income-streams  of  two  kinds  of 
property  bought  and  sold,  the  discrepancy  between  what 
was  expected  and  what  is  actually  realized  may  be 
still  wider.  But,  viewed  in  the  present,  the  estimated 
value  of  the  future  return  is  still  the  equivalent  of  the 
sacrifice.  The  present  value  of  a  future  uncertain  event  is 
equal  to  its  mathematical  value  multiplied  by  a  caution 
factor,^  and  the  mathematical  value  is  equal  to  the  expected 
value  multiplied  by  a  probability  factor  and  discounted 
according  to  the  rate  of  preference  for  present  over  future 
income. 

§  8 

We  thus  see  that  instead  of  the  series  of  simple  equalities 
which  we  found  to  hold  true  in  the  vacuum  where  risk  was 
absent,  we  have  only  a  tendency  toward  equalities,  interfered 
with  by  the  limitations  of  the  loan  market,  and  therefore 
resulting  in  a  series  of  inequalities.  Rates  of  interest, 
rates  of  preference,  and  rates  of  return  on  sacrifice  are  only 
ideally,  not  really,  equal. 

We  conclude  by  summarizing  in  the  following  table  the 
interest-determining  conditions  for  our  tliree  successive 
approximations :  — 

'  See  The  Nature  of  Capital  and  Income,  Chap.  XVI,  §  6. 


5ec.  8] 


THIRD  APPROXIMATION 


221 


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222  THE  RATE  OF   INTEREST  [Chap.  XI 

In  the  first  approximation,  conditions  1  and  4  are  in- 
serted to  complete  the  correspondence  with  the  other  two 
approximations;  but  they  are  both  really  the  same  con- 
dition, and  merely  reexpress  the  hypothesis  under  which 
the  first  approximation  was  made.  It  is  the  remaining 
four  conditions  which  are  of  real  significance. 

The  first  two  approximations  were,  of  course,  merely  pre- 
paratory to  the  third,  which  alone  corresponds  to  the  actual 
world  of  facts.  Yet  the  other  two  approximations  are  of 
equal  importance  with  the  third  from  the  point  of  view  of 
analysis.  They  tell  us  what  would  happen  if  future  income 
were  (1)  fixed  and  certain,  and  (2)  flexible  but  certain; 
and  to  know  what  would  happen  under  these  hypothetical 
conditions  enables  us  better  to  understand  what  does  happen 
under  actual  conditions,  just  as  the  knowledge  that  a  pro- 
jectile would  follow  a  parabola  if  it  were  in  a  vacuum,  and 
that  it  would  follow  a  certain  other  curve  if  in  a  still  at- 
mosphere of  given  density,  enables  the  student  of  practical 
gimnery  better  to  understand  the  actual  behavior  of  his 
cannon  balls.  In  fact,  no  scientific  law  is  a  perfect  state- 
ment of  what  does  happen,  but  of  what  would  happen  if 
certain  conditions  existed  which  do  not  actually  exist.* 
Science  consists  of  the  formulation  of  hypothetical  se- 
quences, not  of  historical  facts;  though  by  successive 
approximations  the  hypotheses  may  be  made  nearly  to 
coincide  with  reality.' 

^  See  the  writer's  "Economics  as  a  Science,"  Science,  August  31, 
1906. 

^  See  Appendix  to  Chap.  XI,  §  1. 


PART   IV.     Conclusions 


Chapter  XII. 

Chapter  XIII. 

Chapter  XIV. 

Chapter  XV. 

Chapter  XVI. 

Chapter  XVII. 


Role  of  Interest  in  Economic  Theory 
Application  to  Actual  Conditions 
Inductive  Verification  (monetary) 
Inductive  Verification  (economic) 
Inductive      Refutation      op      "Money 

Theory" 
Summary 


CHAPTER  XII 

ROLE   OF  INTEREST  IN   ECONOMIC  THEORY 

§1 

Having  shown  how  the  rate  of  interest  is  determined, 
we  have  reached  the  goal  which  we  have  set  ourselves  in  the 
present  book.  But,  though  this  goal  marks  the  end  of  the 
present  inquiry,  it  is  also  the  starting-point  for  other  eco- 
nomic inquiries  of  the  greatest  importance.  We  cannot 
attempt  in  this  book  to  explore  the  fields  which  would  thus 
open  out,  but  in  the  present  chapter  we  shall  indicate 
briefly  what  they  are. 

The  rate  of  interest  plays  a  central  role  in  two  great 
branches  of  economic  science,  —  the  theory  of  prices,  and 
the  theory  of  distribution.  The  role  of  the  rate  of  inter- 
est in  the  theory  of  prices  applies  to  the  determination  of  the 
price  of  wealth,  property,  and  services. 

As  was  shown  in  The  Nature  of  Capital  and  Income,  the 
price  of  any  article  of  wealth  or  property  is  equal  to  the 
discounted  value  of  its  expected  future  services.  If  the 
value  of  these  services  remains  the  same,  a  rise  or  fall  in 
the  rate  of  interest  will  consequently  cause  a  fall  or  rise 
respectively  in  the  value  of  all  instruments  of  wealth.  The 
extent  of  this  fall  or  rise  will  be  the  greater  the  further 
into  the  future  the  services  of  wealth  extend.^  Thus,  land, 
from  which  services  are  expected  to  accrue  uniformly  and 
forever,  will  be  doubled  in  value  if  the  rate  of  interest  is 
halved,  or  halved  in  value  if  the  rate  of  interest  is  doubled. 
In  the  case  of  dwellings,  however,  the  life  of  which  is 
limited,  if  the  rate  of    interest  is  doubled,    the   price  of 

'  See  The  Nature  of  Capital  and  Income,  Chap.  XIII. 
Q  225 


226  THE  RATE  OF  INTEREST  [Chap.  XII 

dwellings  will  fall  less  than  half,  and  if  the  rate  of 
interest  is  halved,  the  price  of  dwellings  will  rise  to  less 
than  double.  In  the  ease  of  furniture  the  fluctuations  in 
value  will  be  even  less  extensive,  and  so  through  the  list 
of  less  durable  commodities,  such  as  clothing,  to  those  of 
very  perishable  types,  such  as  food,  the  value  of  which  will 
not  be  sensibly  affected  by  a  variation  in  the  rate  of  interest. 


As  to  the  influence  of  the  rate  of  interest  on  the  price  of 
services,  we  first  observe  that  services  may  be  intermediate 
or  final.^  The  value  of  intermediate  services  or  "inter- 
actions" is  derived  from  the  succeeding  future  services 
to  which  they  respectively  lead.  For  instance,  the  value 
to  a  farmer  of  the  services  of  his  land  in  affording  pasture 
for  sheep  will  depend  upon  the  discounted  value  of  the  serv- 
ices of  the  flock  in  producing  wool.  If  he  rents  the  land, 
he  will  calculate  what  he  can  afford  to  pay  for  it  on  the 
basis  of  the  value  of  the  wool  which  he  would  expect  to 
obtain  from  his  flock.  In  like  manner,  the  value  of  the 
wool-output  to  the  woolen  manufacturer  is  in  turn  in- 
fluenced by  the  discounted  value  of  the  output  of  woolen 
cloth  to  which  it  contributes.  In  the  next  stage,  the  value 
of  the  production  of  woolen  cloth  will  depend  upon  the 
discounted  value  of  the  income  from  the  production  of 
woolen  clothing.  Finally,  the  value  of  the  last  named  will 
depend  upon  the  expected  income  which  the  clothing  will 
bring  to  those  who  wear  it,  —  in  other  words,  upon  the  use 
of  the  clothes. 

Thus  the  final  services,  consisting  of  the  use  of  the  clothes,  ' 
will  have  an  influence  on  the  value  of  all  the  anterior  serv- 
ices  of   tailoring,  manufacturing   cloth,  producing   wool, 
and  pasturing  sheep,  while  each  of  these  anterior  services, 

*  See  The  Nature  of  Capital  and  Income,  Chap.  IX.    The  subject 
has  already  been  referred  to  in  the  present  volume.  Chap.  VIII. 


Sec.  2]     ROLE  OF  INTEREST  IN  ECONOMIC  THEORY    227 

when  discounted,  will  give  the  value  of  the  respective  capital 
which  yields  them ;  namely,  the  clothes,  cloth,  wool,  sheep, 
and  pasture.  We  find,  therefore,  that  not  only  all  articles 
of  wealth,  but  also  all  the  intermediate  services  ("interac- 
tions") which  they  render,  are  dependent  upon  final  enjoy- 
able uses,  and  are  linked  to  these  final  uses  by  the  rate  of 
interest.  If  the  rate  of  interest  rises  or  falls,  this  chain  will 
shrink  or  expand.  The  chain  hangs,  so  to  speak,  from  its 
final  link  of  enjoyable  services,  and  its  shrinkage  or  ex- 
pansion will  therefore  be  most  felt  by  the  links  most  distant 
from  these  final  services.  A  change  in  the  rate  of  interest 
will  affect  but  slightly  the  price  of  making  clothing,  but 
it  will  affect  considerably  the  price  of  pasturing  sheep. 

A  study,  therefore,  of  the  theory  of  prices  involves  (1) 
a  study  of  the  laws  which  determine  the  final  services  on 
which  the  prices  of  anterior  interactions  depend;  (2)  a 
study  of  the  prices  of  these  anterior  interactions,  as  de- 
pendent, through  the  rate  of  interest,  on  the  final  services ; 
(3)  a  study  of  the  price  of  capital  instruments  and  capital 
property  as  dependent,  through  the  rate  of  interest,  upon 
the  prices  of  their  services.  The  first  study,  which  seeks 
merely  to  determine  the  laws  regulating  the  price  of  final 
services,  is  relatively  independent  of  the  rate  of  interest. 
The  second  and  third,  which  seek  to  show  the  dependence 
on  final  services  of  the  anterior  services  and  of  the  capitals 
which  bear  them,  involve  and  depend  upon  the  rate  of 
interest.  Under  this  second  study  will  fall,  as  a  special 
case,  the  study  of  the  determination  of  economic  rent, 
both  the  rent  of  land  and  the  rent  of  other  instruments  of 
wealth.  Thus,  the  rent  of  the  pasture  referred  to,  consist- 
ing, as  it  does,  of  the  value  of  the  services  of  pasturing, 
is  dependent,  through  the  rate  of  interest,  upon  the  dis- 
counted value  of  the  future  final  services  to  which  the  land 
contributes.  It  is  clear,  then,  that  the  rent  of  the  land 
is  partly  dependent  upon  the  rate  of  interest,  and  that  the 
same  dependence  applies  to  the  rent  of  any  other  instru- 
ment. 


228  THE  RATE  OF   INTEREST  [Chap.  XII 

§3 

Similar  considerations  apply  to  the  determination  of  the 
rate  of  wages.  So  far  as  the  employer  is  concerned,  the 
payment  of  wages  to  a  workman  represents  the  value  of 
his  services.  These  services  are  interactions  or  inter- 
mediate services  leading  to  some  future  enjoyable  service. 
Thus,  the  shepherd  hired  by  the  farmer  to  tend  the  sheep 
in  the  pasture  renders  services  the  value  of  which  to  the 
farmer  is  estimated  in  precisely  the  same  way  as  the  value 
of  the  services  of  the  land  which  he  hires.  It  follows  that 
the  rate  of  wages  is  dependent  upon  the  rate  of  interest, 
and,  conformably  to  the  previous  reasoning,  the  dependence 
of  wages  on  the  rate  of  interest  is  the  more  pronounced  the 
more  remote  are  the  ultimate  services  to  which  the  work 
of  the  laborer  leads.  As  stated  in  Chapter  IX,  in  a  com- 
munity where  the  workmen  are  largely  employed  in  enter- 
prises requiring  a  long  time,  such  as  digging  tuimels  and 
constructing  other  great  engineering  works,  the  rate  of 
wages  will  tend  to  fall  appreciably  with  a  rise  in  the  rate 
of  interest,  and  to  rise  appreciably  with  a  fall  in  the  rate 
of  interest;  whereas  in  a  coimtry  where  the  laborers  are 
largely  engaged  in  personal  services  or  in  other  work  which 
is  not  far  distant  from  the  final  goal  of  enjoyable  services, 
a  change  in  the  rate  of  interest  will  affect  the  rate  of  wages 
but  slightly. 

What  has  been  said,  however,  applies  only  to  wages  from 
the  standpoint  of  the  employer.  The  rate  of  wages  is 
dependent  upon  supply  as  well  as  demand ;  that  is,  upon  the 
willingness  of  the  workman  to  offer  his  services,  as  well  as 
upon  the  desire  of  the  employer  to  secure  them.  From  the 
standpoint  of  the  laborer,  wages  constitute  an  incentive  to 
exertion  or  labor.  This  exertion  is,  as  we  have  seen,  a  final 
disservice,  and  its  value  is  not  determined  by  the  rate  of 
interest  in  the  manner  of  services  which  are  intermediate. 
It  is  a  great  mistake  to  treat  the  subject  of  wages,  as  many 
authors  do,  exclusively  from  the  employer's  standpoint. 


Sec.  4]    ROLE  OF  INTEREST  IN  ECONOMIC  THEORY     229 

Our  purpose  here,  however,  is  not  to  enter  into  an  extended 
discussion  of  the  theory  of  wages,  but  merely  to  show  at 
what  points  in  that  theory  the  rate  of  interest  enters,  and 
at  what  points  it  does  not  enter. 

§  4 

The  second  great  branch  of  economics  to  which  the  rate 
of  interest  appHes  is  the  theory  of  distribution.  In  the 
classical  political  economy,  the  relation  of  the  rate  of  in- 
terest to  distribution  was  entirely  misconceived.  Dis- 
tribution was  erroneously  regarded  as  a  separation  of  the 
income  of  society  into  "interest,  rent,  wages,  and  profits." 
By  "interest"  of  course  was  meant,  not  the  rate  of  interest, 
but  the  rate  of  interest  multiplied  by  the  value  of  the  capi- 
tal "yielding  interest,"  But  we  have  seen  that  the  value 
of  the  capital  is  found  by  taking  the  income  which  it  yields 
and  capitalizing  it  by  means  of  the  rate  of  interest.  To 
reverse  this  process,  and  obtain  the  income  by  multiplying 
the  capital  by  the  rate  of  interest,  is  proceeding  in  a  circle. 
The  result  of  multiplying  capital  by  the  rate  of  interest, 
i.e.  income,  is  not  really  a  complex  product  of  two  factors, 
but,  on  the  contrary,  is  the  single  original  factor, — income. 
We  have  seen  in  this  book  that  it  is  this  income  which 
affords  the  basis  for  the  determination  of  the  rate  of  interest, 
and,  through  the  rate  of  interest,  of  capital  value.  The 
income-stream  of  society  is  the  ultimate  and  basic  fact  from 
which  the  whole  economic  fabric  should  be  constructed. 
All  of  this  income  springs  from  capital-wealth,  if  land  and 
man  are  included  in  that  term,  or  if  not,  from  capital  and 
man,  or  capital,  land,  and  man.  It  may  all  be  capitalized, 
and  hence,  if  we  follow  the  definition  of  capital  adopted  in 
this  book,  it  may  all  be  regarded  as  interest  upon  the  capital- 
value  thus  found.  Hence  "interest"  is  not  a  part,  but  the 
whole,  of  income.  It  includes  what  is  called  rent  and  profits, 
and  even  wages;  for  the  income  of  the  workman  may 
be   capitalized   quite  as  truly  as  the  income  of  land  or 


230  THE  RATE  OP  INTEREST  [Chap.  XII 

machinery.  Thus,  so  far  from  having  "interest,  rent, 
wages,  and  profits"  as  mutually  exclusive  portions  of  in- 
come, we  see  that  "interest"  includes  all  four.  The  error 
of  the  classical  economists  and  of  their  modern  followers 
in  distinguishing  between  interest,  rent,  etc.,  as  separate 
but  coordinate  incomes,  is  partly  due  to  the  failure  to 
perceive  that  whereas  all  income  springs  from  capital- 
wealth,  yet  capital-value  springs  from  income. 

Another  oversight  closely  associated  with  the  last  is 
that  by  which  rent  and  wages  were  conceived  as  deter- 
mined independently  of  the  rate  of  interest,  whereas  we  have 
just  seen  that  the  rate  of  interest  enters  as  a  vital  element 
into  the  determination  of  both. 

We  shall,  therefore,  in  discussing  the  theory  of  distribu- 
tion, abandon  the  "classical"  point  of  view  entirely.  And 
little  regret  should  be  caused  by  such  abandonment,  for  the 
concept  of  distribution  which  the  classical  economists  have 
given  us  is  quite  incompatible  with  the  ordinary  conception 
of  the  term.  The  phrase  "distribution  of  wealth"  implies 
ordinarily,  or  should  imply,  the  problem  of  the  relative 
wealth  of  individuals,  —  the  problem  of  the  rich  and  the 
poor.*  But  the  separation  of  the  aggregate  income  into 
four  abstract  magnitudes  has  little  to  do  with  the  question 
of  how  much  income  the  different  individuals  in  society 
receive.  Were  it  true  that  society  consisted  of  four  inde- 
pendent and  mutually  exclusive  groups,  —  laborers,  land- 
lords, entrepreneurs  and  capitalists,  —  the  fourfold  defi- 
nition would  have  some  connection  with  the  actual  dis- 
tribution of  wealth.  But,  in  fact,  the  entrepreneur  is 
almost  invariably  a  "capitalist";  i.e.  is  the  owner  of  other 
capital  than  land;  the  "capitalist"  is  frequently  a  landlord, 
or  vice  versa;  and  even  the  laborer  is  to-day  often  a  small 
capitalist.  It  is  true  that  a  century  ago  in  England  the 
lines  of  social  classification  corresponded  roughly  and  to 
some  extent,  at  least,  with  the  abstract  divisions  into  which 

*  Cf.  Edwin  Cannan,  "  The  Division  of  Income,"  Quarterly  Journal 
of  Economies,  May,  1905. 


Sec.  6]    ROLE  OF  INTEREST  IN  ECONOMIC  THEORY     231 

economists  separated  income;  but  this  fact  is  of  interest 
only  in  explaining  historically  the  origin  of  the  classical 
theory  of  distribution/ 

§5 

Turning  to  the  true  problem  of  distribution,  that  of  de- 
termining the  amounts  of  capital  and  income  possessed  by 
different  individuals  in  society,  we  find  that  economists 
have  contributed  extremely  little  to  its  solution.  A 
statistical  beginning  has  been  made  by  Professor  Pareto 
in  his  interesting  "curves  of  distribution  of  income,"^ 
in  which  he  shows  the  surprising  result  that  in  all  cases 
where  figures  are  available,  the  relative  distribution  of 
incomes  is  fairly  uniform  in  different  times  and  places. 
So  far  as  the  philosophical  theory  of  distribution  is  con- 
cerned, the  only  writer  who  seems  to  have  contributed 
materially  to  the  subject  is  John  Rae.'  He  showed  that 
persons  who  had  naturally  what  we  have  called  in  this  book 
a  low  rate  of  preference  for  present  over  future  income 
tended  to  grow  rich,  whereas  those  who  had  the  opposite 
trait  tended  to  grow  poor. 

We  saw  in  a  previous  chapter  that  the  rates  of  prefer- 
ence among  different  individuals  were  equalized  by  borrow- 
ing and  lending  or  buying  and  selling.  In  the  case  of  an 
individual  whose  rate  of  preference  for  present  enjoyment 
was  unduly  high,  we  found  that  he  would  contrive  to  modify 
his  income-stream  by  increasing  it  in  the  present  at  the 
expense  of  the  future.  We  were  then  intent  on  studying 
this  phenomenon  only  on  the  side  of  income ;  but  the  effect 
on  capital  can  be  easily  seen  by  applying  the  principles  of 
The  Nature  of  Capital  and  Income,  Chapter  XIV.  If  a 
modification  of  the  income-stream  is  such  as  to  make  the 
present  rate  of  realized  income  exceed  the  "standard" 

'  Cf .  Edwin  Cannan,  loc.  cit. 

'  Cours  d'Economie  Politique,  Vol.  II,  Lausanne,  1897,  Book  III. 

*  The  Sociological  Theory  of  Capital,  Chap.  XIII. 


232  THE   RATE  OF  INTEREST  [Chap.  XII 

income,  capital  must  be  depleted  to  the  extent  of  the  excess, 
and  the  individual  will  grow  poor.  This  may  be  brought 
about  by  borrowing  immediate  income  and  paying  future 
income,  or  by  selling  those  instruments  the  income  of  which 
is  far  distant,  and  buying  those  which  have  more  immediate 
returns.  Individuals  of  the  type  of  Rip  Van  Winkle,  if  in 
possession  of  land  and  other  durable  instruments,  will  either 
sell  or  mortgage  them  in  order  to  secure  the  means  for 
obtaining  enjoyable  services  more  rapidly.  The  effect  will 
be,  for  society  as  a  whole,  that  those  individuals  who  have 
an  abnormally  low  appreciation  of  the  future  and  its  needs 
will  gradually  part  with  the  more  durable  instruments, 
and  that  these  will  tend  to  gravitate  into  the  hands  of  those 
who  have  the  opposite  trait.  By  this  transfer  an  in- 
equality in  the  distribution  of  capital  is  gradually  effected, 
and  this  inequality,  once  achieved,  tends  to  perpetuate 
itself.  The  poorer  a  man  grows  the  more  keen  his  apprecia- 
tion of  present  goods  is  likely  to  become.  When  once  the 
spendthrift  is  on  the  downward  road,  he  is  likely  to  continue 
in  the  same  direction.  When  he  has  succeeded  in  losing 
all  his  capital  except  his  own  person,  the  process  usually 
comes  to  an  end,  because  society,  in  self-protection,  decrees 
that  it  shall  go  no  further.  But  where  there  is  no  such 
safeguard,  the  unfortunate  victim  may  sink  into  even  lower 
stages  of  debt  servitude,  as  in  Java'  or  Russia.  Reversely, 
when  the  accumulator  is  well  advanced  in  his  accumulations, 
his  rate  of  preference  for  the  present  diminishes  still  further, 
and  accumulation  becomes  still  easier.  Hence,  in  some 
countries  the  rich  and  poor  come  to  be  widely  and  per- 
manently separated,  the  former  constituting  a  hereditary 
aristocracy  and  the  latter  a  helpless  and  degraded  peas- 
antry. 

Fortunately,  however,  another  factor  enters  which  tends 
to  counteract  these  tendencies.  This  is  the  effect  of  habit. 
It  has  already  been  noted  that  one's  rate  of  preference  for 

*  See  Prof.  Clive  Day,  The  Dutch  in  Java,  New  York  (Macmillan), 
1904,  Chap.  X. 


Sec.  5]    ROLE   OF   INTEREST  IN  ECONOMIC  THEORY     233 

present  over  future  income,  given  a  certain  income-stream, 
will  be  high  or  low  according  to  the  past  habits  of  the  in- 
dividual. If  he  has  been  accustomed  to  simple  and  inex- 
pensive ways  he  finds  it  fairly  easy  to  save  and  ultimately 
accumulate  a  little  property.  The  habits  of  thrift  being 
transmitted  to  the  next  generation  result  in  still  further 
accumulation,  until,  in  the  case  of  some  of  the  descendants, 
affluence  or  great  wealth  may  result.  Reversely,  if  a  man 
has  been  brought  up  in  the  lap  of  luxury  he  will  have  a 
keener  desire  for  present  enjoyment  than  if  he  had  been 
accustomed  to  the  simple  living  of  the  poor.  The  effect  of 
this  factor  is  that  the  children  of  the  rich,  who  have  been 
accustomed  to  luxurious  living  and  who  have  inherited  only 
a  fraction  of  their  parents'  means,  will,  in  attempting  to 
keep  up  the  former  pace,  be  compelled  to  check  the  accumu- 
lation and  even  to  start  the  opposite  process  of  the  dissipa- 
tion of  their  family  fortune.  In  the  next  generation  this 
reverse  movement  is  likely  to  gather  headway  and  to 
continue  until,  with  the  gradual  subdivision  of  the  fortune 
and  the  increasing  reluctance  of  the  successive  generations 
to  curtail  their  expenses,  in  the  third  or  fourth  generation 
there  comes  a  return  to  actual  poverty.  It  thus  often 
happens  that  there  is  a  tendency  for  the  accumulation  and 
dissipation  of  wealth  to  occur  in  cycles.  If  there  is  the 
conjunction  of  favorable  circumstances,  as  thrift,  abihty, 
and  good  fortune,  a  few  individuals  will  rise  from  the 
lower  ranks.  They  accumulate  a  few  thousand  dollars, 
which,  mider  like  favoring  circumstances,  in  the  next  gen- 
eration or  two  may  become  several  millions.  Then  the 
unfavorable  effects  of  luxury  begin,  and  in  an  equal  num- 
ber of  generations  the  majority  of  the  heirs  have  returned 
to  the  level  at  which  their  ancestors  began.  An  old  adage 
has  stated  this  observation  in  the  form,  ''From  shirt  sleeves 
to  shirt  sleeves  in  four  generations."  This  cyclical  move- 
ment is  more  apt  to  occm'  in  countries  like  the  United 
States,  where,  owing  to  the  rapidly  changing  conditions, 
there  is  a  larger  number  of  opportunities  either  for  rising 


234  THE  RATE  OF  INTEREST  [Chap.  XII 

or  falling  in  the  economic  scale.  Where,  as  in  the  older 
countries  of  Europe,  conditions  have  become  fixed  and  less 
favorable  to  changes  of  any  kind,  the  tendency  of  the 
distribution  of  wealth  is  to  remain  relatively  imchanged. 
This  is  especially  true  where,  as  in  England,  the  customs 
as  to  the  inheritance  of  property  have  tended  to  keep 
large  fortunes  intact  in  the  hands  of  the  eldest  son. 

§6 

In  the  general  causation  of  distribution  which  has  thus 
been  outlined,  the  central  role  is  played  by  the  individual 
rate  of  preference  for  present  over  future  income,  which, 
as  we  have  seen,  is  the  subjective  prototype  of  the  rate  of 
interest.  The  study  of  the  theory  of  interest,  therefore, 
lays  the  foundation  for  a  study  of  the  theory  of  distribution. 
The  objective  rate  of  interest  represents  the  norm  to  which 
the  individual  adjusts  his  rate  of  preference  for  present 
over  future  income,  and  in  this  adjustment  he  changes  his 
economic  status  for  better  or  worse.  The  existence  of  this 
general  market  rate  of  interest  to  which  he  adjusts  his  rate 
of  preference  supplies  an  easy  highway  for  the  movement  of 
his  fortune  in  one  direction  or  the  other.  If  an  individual 
has  spendthrift  tendencies,  their  indulgence  is  facilitated 
by  access  to  a  loan  market;  and  reversely,  if  he  desires  to 
save,  he  may  do  so  the  more  easily  if  there  is  a  market  for 
savings.  The  irregularities  in  the  distribution  of  capital 
are  thus  due  to  the  opportunity  to  effect  exchanges  of  parts 
of  the  income-stream  separated  in  time.  The  rate  of 
interest  is  simply  the  market  price  for  such  exchange. 
By  means  of  this  market  price,  both  those  who  wish  to 
barter  present  for  future  income  and  those  who  wish  to 
do  the  reverse,  may  satisfy  their  desires.  The  one  will 
gradually  increase,  and  the  other  decrease,  his  capital. 
If  all  individuals  were  hermits,  it  would  be  much  more  diffi- 
cult either  to  accumulate  or  to  dissipate  fortunes,  and  the 
distribution  of  wealth  would  therefore  be  much  more  even. 


Sec.  6]    ROLE  OF  INTEREST  IN  ECONOMIC  THEORY     235 

Inequality  arises  out  of  the  exchange  of  income,  carrying 
some  individuals  toward  wealth  and  others  toward  poverty. 
The  inequality  of  wealth  is  facilitated  by  the  existence  of  a 
loan  market.  In  a  sense,  then,  it  is  true,  as  the  socialist 
maintains,  that  inequality  is  due  to  social  arrangements; 
but  the  arrangements  to  which  it  is  due  are  not,  as  he  as- 
sumes, primarily  such  as  take  away  the  opportunity  to  rise 
in  the  economic  scale ;  they  are  the  contrary  arrangements 
which  facilitate  both  rising  and  falling,  according  to 
the  choice  of  the  individual.  The  improvident  sink  like 
lead  to  the  bottom.  Once  there,  they  or  their  children  find 
difficulty  in  rising.  Accumulation  is  a  slow  process,  and 
especially  slow  when  the  great  numbers  of  the  poor  have, 
by  competition,  reduced  the  values  of  their  services  so  low 
that  the  initial  saving  becomes  almost  impossible. 

This  is  not  the  place  for  following  out  these  tendencies 
and  their  sociological  effects,  nor  need  we  stop  to  answer 
the  many  questions  which  arise  in  such  an  inquiry,  such  as, 
What  is  the  effect  of  a  change  in  the  rate  of  interest  in 
stimulating  or  discouraging  the  accumulation  or  dissipation 
of  capital  ?  ^  Or,  What  is  the  effect  on  the  poor  of  the  luxu- 
rious habits  of  the  rich  ?  Nor  are  we  concerned  with  the 
other  factors  which  influence  the  distribution  of  wealth, 
but  which  do  not  involve  the  rate  of  interest.  We  are  at 
present  content  merely  to  prepare  the  way  for  their  answer 
by  indicating  the  nature  of  the  problems  and  the  relation 
of  the  theory  of  interest  to  them. 

'  See  E.  C.  K.  Conner,  Interest  and  Saving,  London  (Macmillan), 
1906. 


CHAPTER  XIII 


APPLICATION  TO  ACTUAL  CONDITIONS 


§    1 

We  have  now  completed  the  formal  statement  of  our 
theory  of  interest.  It  remains  to  show  in  what  way  this 
theory  may  be  brought  into  connection  with  actual  experi- 
ence. For  this  purpose  we  need  first  to  classify  the  various 
forms  which  interest  takes. 

We  have  seen  that  the  rate  of  interest  discloses  itself 
in  two  ways;  namely,  as  explicit  and  implicit  interest. 
We  begin  with  explicit  interest,  or  the  interest  in  a  loan 
contract.  From  the  standpoint  of  the  borrower,  loan  con- 
tracts may  be  classified  as  follows : — 


f 


Loans 


For  private 
purposes 

For  public 
purposes 
(municipal, 
etc.) 


r 


For  business 
purposes 


To  offset  misfortune  or  improvidence. 
To  offset  fluctuations  in  income  and  outgo. 
To  anticipate  improvement  in  financial  con- 
dition. 

'  For  military  purposes. 
To  offset  fluctuations  in  revenue  and  ex- 
penses. 
For  public  improvements. 
''  Crop  liens. 
Commercial  paper. 
Accommodation  paper. 
Call  loans. 

Mortgages  on  farms. 

Mortgages  on  city  real 
estate. 

Mortgage  bonds  of  cor- 
porations. 

Debentures  of  corpora- 
tions. 

236 


Short  or 
periodic . 
loans 


Long  or  per- 
manent loans ' 


Sec.  1]         APPLICATION  TO  ACTUAL  CONDITIONS  237 

Private  loans  are  loans  of  individuals  for  personal  purposes 
other  than  those  arising  out  of  business  relations.  Of  these, 
loans  contracted  because  of  misfortune  or  improvidence, 
though  to-day  constituting  a  very  small  fraction  of  total 
indebtedness,  represent  probably  the  original  type  of  loan. 
It  was  against  such  loans  that  the  biblical,  classical,  and 
mediaeval  prohibitions  and  regulations  were  directed,  and 
it  is  only  against  them  to-day  that,  in  enlightened  com- 
munities, regulations  affecting  the  rate  of  interest  still 
survive.  It  is  such  loans  that  supply  most  of  the  business 
to  pawn  shops,  the  patrons  of  which  are  usually  victims 
of  misfortune  or  improvidence.  It  is  clear  that  the  theory 
of  interest  which  has  been  propounded  applies  to  this 
species  of  loan.  Sickness  or  death  in  one's  family,  or  losses 
from  fire,  theft,  flood,  shipwreck,  or  other  causes,  make 
temporary  inroads  upon  one's  income.  It  is  to  tide  over 
such  a  stringency  in  income  that  the  loan  is  contracted. 
It  ekes  out  the  less  adequate  income  of  the  present  by 
sacrificing  something  from  the  more  adequate  income  ex- 
pected in  the  future.  Similar  principles  apply  to  the  spend- 
thrift, who,  though  not  a  victim  of  accidental  misfortune, 
brings  misfortune  upon  himself.  He  borrows  in  order  to 
supplement  an  income  inadequate  to  meet  the  require- 
ments which  he  has  set  himself,  while  he  trusts  for  repay- 
ment to  the  shadowy  resources  of  a  distant  future.  It  is 
evident,  therefore,  that  the  loans  just  described  are  made 
for  the  sake  of  correcting  an  income  curve  the  time-shape 
of  which  is  inconvenient  or  intolerable. 

The  second  class  of  personal  loans  comprises  those  grow- 
ing out  of  such  fluctuations  in  income  as  are  not  due  to 
misfortune  or  improvidence.  Many  persons  receive  their 
money-income  in  very  irregular  and  unequal  instalments, 
while  their  money  outgo  may  likewise  have  an  irregular 
time-schedule.  Unless  the  two  sides  of  the  account  happen 
to  synchronize,  the  individual  will  be  alternately  "short" 
and  "flush."  Thus,  if  he  receives  his  largest  dividends  in 
January,  but  has  to  meet  his  largest  expenses,  let  us  say 


238  THE  RATE  OF  INTEREST  [Chap.  XIII 

taxes,  in  September,  he  is  likely  to  borrow  at  tax  time  for 
the  ensuing  four  months,  in  anticipation  of  the  January 
dividends.  That  is,  he  borrows  at  a  time  when  his  income- 
stream  would  otherwise  be  low,  and  repays  at  a  time  when 
it  would  otherwise  be  high.  The  effect  is  to  level  up  the 
fluctuations  of  his  income. 

The  third  class  of  personal  loans  comprises  those  which 
grow  out  of  large  expected  additions  to  income.  Heirs 
to  a  fortune  sometimes  borrow  in  anticipation  of  their 
bequests.  A  considerable  volume  of  such  loans  has  un- 
doubtedly been  contracted,  especially  in  Great  Britain. 
The  borrower  in  this  case  is  evidently  trying  to  enjoy  in  the 
present  some  of  the  income  which  is  promised  for  the  future ; 
in  other  words,  to  alter  the  time-shape  of  his  income-stream 
in  accordance  with  his  desires.  The  same  motives  actuate 
young  men  preparing  for  life,  and  explain  the  loans  which 
are  often  contracted  by  them  for  defraying  the  expenses 
of  education.  It  was  for  such  persons  that  Benjamin 
Franklin  left  his  peculiar  bequests  to  the  cities  of  Phil- 
adelphia and  Boston  in  1790.  To  each  he  bequeathed 
£1000  to  be  lent  out  in  small  sums  at  5  per  cent,  to  young 
married  "artificers."  The  sums  repaid  were  to  be  added 
to  the  fund  and  again  lent. 

§2 

In  the  case  of  public  loans,  we  find  the  same  general 
principles  in  operation  which  we  have  just  seen  to  apply  to 
private  loans.  By  a  public  loan  is  meant  a  loan  contracted 
by  a  public  corporation  or  association,  such  as  a  state, 
county,  municipality,  school  district,  or  other  administrative 
unit,  as  well  as  such  quasi-public  institutions  as  churches, 
hospitals,  and  public  libraries.  Public  loans  may  be  sub- 
divided into  three  classes :  (1)  those  growing  out  of  military 
exigencies ;  (2)  those  growing  out  of  fluctuations  in  income ; 
(3)  those  growing  out  of  need  for  public  improvements. 

The  first  class,  loans  for  war  and  war  preparation,  cor- 
responds to  the  case  first  considered  under  private  loans,  — ■ 


Sec.  2]        APPLICATION  TO   ACTUAL  CONDITIONS  239 

loans  growing  out  of  misfortune.  Ordinarily  the  expenses 
of  government  are  defrayed  out  of  taxes,  which  constitute 
a  regular  deduction  from  the  incomes  of  the  taxpayers; 
but  war  brings  with  it  extraordinary  expenses  which  must 
be  met  by  extraordinary  means.  If  the  cost  of  war  were 
wholly  defrayed  by  taxes,  the  taxpayers  would  suffer  large 
and  sudden  reductions  in  their  incomes  for  the  time  being. 
They  prefer  instead  to  place  some  of  the  burden  on  the 
future,  —  even  upon  posterity.  This  is  accomplished  by 
war  loans,  to  be  repaid  many  years  after  the  war  is  over. 
Thus,  so  far  as  the  taxpayers  are  concerned,  the  expense 
of  the  war  is  spread  over  a  considerable  time,  and  the  im- 
mediate reduction  in  their  income-stream,  which  would 
otherwise  be  caused  by  the  war,  is  avoided.  But  for  the 
world  as  a  whole  this  is  not  true ;  for  others  than  the  tax- 
payers, namely,  the  bondholders,  must  bear  the  brunt  of 
the  reduction  in  the  world's  incomie-stream  which  the  war 
has  brought  about.  It  follows  that  the  issue  of  bonds  has 
as  its  ultimate  effect,  not  a  postponement  of  the  cost  of  the 
war,  but  its  shifting  from  one  class  to  another.  We  thus 
see  that  war  loans  clearly  exemplify  the  theory  of  loans 
which  has  been  elaborated.  The  need  for  such  loans  grows 
out  of  an  impending  depression  in  the  income-stream  of 
the  taxpayers. 

The  second  class  of  public  loans,  namely,  loans  due  to 
fluctuations  in  public  receipts  and  disbursements,  corre- 
sponds to  the  second  class  of  private  loans.  A  government 
receives  its  income  chiefly  in  taxes,  and  only  once  a  year, 
whereas  its  outgo  occurs  day  by  day  and  month  by  month. 
It  thus  happens  that  a  government  is  alternately  accumulat- 
ing a  large  surplus  and  suffering  a  large  deficit.  The  in- 
convenient effects  of  this  have  been  often  commented  upon, 
especially  in  this  country,  where  the  Treasury  for  half  a 
century  has  been  relatively  independent  of  institutions 
of  credit.*    This  inconvenience  may  be  largely  avoided  by 

'  See  David  Kinlcy,  The  Independent  Treasury  of  the  United  States, 
Boston  (Crowell),  1893. 


240  THE  RATE  OF  INTEREST  [Chap.  XIII 

a  business  relation  between  the  government  and  some  in- 
stitutions of  credit,  as,  for  instance,  in  England,  between 
the  government  and  the  Bank  of  England.  The  govern- 
ment may  correct  the  irregularities  in  its  income-stream 
either  by  borrowing  for  current  expenses  in  anticipation  of 
taxes,  or  by  lending  at  interest ;  that  is,  depositing  the  taxes 
when  first  received,  in  anticipation  of  the  expenses  which 
follow. 

The  third  class  of  public  loans  comprises  those  for  public 
improvements,  such  as  the  erection  of  government  build- 
ings, the  improvement  of  roads,  bridges,  and  harbors,  the 
construction  of  municipal  waterworks  or  schoolhouses,  or 
the  prosecution  of  other  government  enterprises.  In  all 
such  cases  it  is  usual  to  finance  the  enterprise  by  issuing 
bonds.  The  reason  clearly  is  that  these  improvements 
constitute  an  extraordinary  cost,  similar  to  the  expense 
of  a  war,  which,  without  the  issue  of  bonds,  would  cause 
a  temporary  depression  in  income-streams.  The  taxpayers 
as  a  whole  cannot  afford  the  first  heavy  drain,  even  with 
the  prospect  of  substantial  benefits  to  follow.  They 
therefore  prefer,  in  place  of  such  a  fluctuating  income- 
stream,  a  more  uniform  one.  To  secure  this  uniformity  is 
evidently  the  purpose  of  the  loan.  We  see,  therefore,  that 
this  class  of  loans  also  exemplifies  the  theory  of  the  re- 
lation of  borrowing  and  lending  to  the  time-shape  of  an 
income-stream. 

§3 

The  third  and  last  general  class  of  loans  is  that  of  business 
loans.  Business  loans  are  loans  growing  out  of  trade. 
They  are  commonly,  though  not  very  felicitously,  called 
"productive  loans,"  whereas  the  loans  which  have  thus  far 
been  considered  would  commonly  be  called  "consumption 
loans."  Business  loans  constitute  by  far  the  most  impor- 
tant class  of  present  indebtedness.  Mr.  George  K.  Holmes 
has  estimated  that  at  least  nine  tenths  of  the  existing  in- 


Sec.  3]         APPLICATION  TO  ACTUAL  CONDITIONS  241 

debtedness  in  the  United  States  was  incurred  for  the  ac- 
quirement of  the  more  durable  kinds  of  property,  leaving 
not  more  than  one  tenth,  and  probably  much  less,  as  a 
"consumption  debt,"  or  a  debt  necessitated  by  misfortune. 
No  theory  of  interest  would  therefore  be  complete  which 
should  fail  to  apply  to  business  loans. 

At  first  sight  it  would  seem  that  the  theory  which  has 
been  given,  depending  as  it  does  on  the  enjoyable  income- 
stream  of  an  individual,  can  apply  only  to  consumption 
loans.  Net  income,  as  was  shown  elsewhere,^  consists 
of  one's  personal  satisfactions,  —  nourishment,  clothing, 
shelter,  and  other  enjoyable  services.  The  loans  of  business 
seem  too  impersonal  to  be  explained  by  a  theory  which 
depends  wholly  on  personal  satisfactions.  In  fact,  it  has 
often  been  said  by  economists,  in  treating  this  subject, 
that  consumption  loans  are  explained  on  quite  other 
principles  than  loans  contracted  in  the  regular  course 
of  commercial  transactions.  Even  Bohm-Bawerk,  in  his 
Positive  Theory  of  Capital,  states  that  consumption  loans 
are  explained  by  the  preference  for  present  enjoyment 
over  future,  but  that  the  loans  of  business  are  chiefly  due 
to  the  "technical  superiority  of  present  goods,"  which 
grows  out  of  the  greater  productiveness  of  lengthy  pro- 
cesses. 

A  little  consideration  will  show,  however,  that  business 
loans  are  not  so  difTerent  from  consumption  loans ;  that  they 
also  are  used  to  tide  over  lean  times  in  anticipation  of  pros- 
perity; and  that  they  are  contracted  to  rectify  the  distor- 
tion of  the  income-stream  which  would  otherwise  result 
from  business  operations.  The  truth  is  —  and  it  should 
never  be  lost  sight  of  —  that  business  men  conduct  their 
business  with  an  eye  always  to  enjoyable  income.  This 
is  the  object  of  all  their  operations,  though  it  may  be  ob- 
scured by  the  interposition  of  the  many  intermediate  steps, 
or  "interactions."  Business  operations  are  not  ends  in 
themselves,  but  means  for  ultimate  personal  enjoyment. 

*  The  Nature  of  Capital  and  Income,  Chaps.  IX,  X. 


242  THE  RATE  OF  INTEREST  [Chap.  XIII 

A  business  man  not  only  conducts  his  business  for  what 
he  can  get  out  of  it  for  personal  use,  but  also  regulates  it  so 
that  what  thus  comes  out  may  accrue  not  in  irregular 
spurts,  but  so  far  as  possible  in  such  a  stream  as  will  sjoi- 
chronize  with  the  exigencies  of  his  home  life.  In  a  sense 
we  may  say,  therefore,  that  it  is  his  home  that  "  runs  "  his 
business  rather  than  his  business  that  "  rmis  "  his  home. 

§4 

In  order  to  see  how  the  theory  of  interest  which  has 
been  explained  applies  to  business  loans,  let  us  consider 
the  two  chief  classes ;  namely,  short  loans,  or  those  growing 
out  of  periodic  variations,  and  long  loans,  or  those  for  rela- 
tively permanent  investment.  The  short  or  periodic  loans 
are  those  which  grow  out  of  the  change  in  the  seasons  and 
the  ebb  and  flow  of  business.  These  loans  are  obtained 
usually  but  once  a  year  at  a  specified  time.  The  ultimate 
cause  is  the  cyclical  change  in  the  position  of  the  earth  in 
reference  to  the  sun.  This  gives  rise  to  the  cycle  of  the 
seasons,  the  effects  of  which  are  felt  not  only  in  agriculture, 
but  in  manufacturing,  transportation,  trade,  and  banking. 
The  alternate  congestion  and  thinning  of  the  freight  busi- 
ness, the  alternate  stocking  and  depletion  of  raw  ma- 
terial in  factories,  the  fluctuations  of  trade  activity,  both 
wholesale  and  retail,  the  transfer  of  bank  deposits  between 
New  York  and  the  West  for  "moving  crops"  or  for  other 
uses,  all  testify  to  the  seasonal  rhythm  which  is  constantly 
felt  in  the  great  network  of  business  operations.  Without 
some  compensating  apparatus  such  as  that  for  borrowing 
and  lending,  these  seasonal  fluctuations  would  transmit 
themselves  to  the  final  enjoyable  income-streams  of  indi- 
viduals, and  those  incomes,  instead  of  constituting  an 
even  flow,  would  accrue  by  fits  and  starts,  a  summer  of 
lavish  enjoyment  being  followed  by  a  winter  on  short 
rations. 

To  show  how  borrowing  and  lending  compensate  for 
these  fluctuations,  we  may  consider  first  what  is  perhaps 


Sec.  4]         APPLICATION  TO  ACTUAL  CONDITIONS  243 

the  most  primitive  type  of  the  short  or  periodic  loan; 
namely,  that  contracted  by  poor  farmers  in  anticipation  of 
crops.  In  the  South  among  the  negroes  this  takes  the 
form  of  what  is  called  a  "crop  lien,"  the  cultivator  borrow- 
ing money  enough  to  enable  him  to  live  until  crop  time  and 
pledging  repayment  from  the  crop.  Here,  evidently,  the 
purpose  of  the  loan  is  to  eke  out  the  meager  income  of 
actual  enjoyments.  The  loan,  in  other  words,  is  for  sub- 
sistence. This  case,  therefore,  is  covered  by  the  theory  of 
interest  which  has  been  given. 

We  proceed  now  to  show  that  this  same  theory  of  interest 
applies  also  to  loans  contracted  in  the  commercial  world  at 
large,  A  short-time  commercial  loan  is  contracted  for  the 
purpose  of  buying  goods,  with  the  expectation  of  repayment 
after  their  sale.  A  common  form  is  what  is  called  "com- 
mercial paper."  A  ready-made  clothing  house  may  buy 
overcoats  in  summer  in  order  to  sell  them  in  the  fall.  If 
these  operations  were  conducted  on  a  strictly  cash  basis, 
the  tendency  would  be  for  the  income  of  the  clothier  to 
suffer  great  fluctuations.  He  could  realize  but  little  during 
the  summer,  on  account  of  the  enormous  expense  of  stock- 
ing-in  for  fall  trade,  whereas  in  the  fall  he  could  obtain  large 
returns  and  live  on  a  more  elaborate  scale.  This  would 
mean  the  alternation  of  famine  and  feast  in  his  family. 
One  way  to  avoid  such  a  result  would  be  to  keep  on  hand  a 
large  supply  of  cash  as  a  buffer  between  the  money-income 
and  personal  expenditure.  In  this  case  the  fluctuations 
would  not  reach  the  stage  of  personal  enjoyment,  but 
would  spend  their  force  in  fluctuations  of  the  volume  of 
cash.  A  more  effective  and  less  wasteful  method  for  the 
merchant,  of  taking  the  kinks  out  of  his  income,  is  by 
negotiating  commercial  paper.  The  clothier,  instead  of 
suffering  the  large  cash  expense  of  stocking-in  in  summer, 
will  make  out  a  note  to  the  manufacturer  of  overcoats. 
After  the  fall  trade,  this  note  is  extinguished,  having 
fulfilled  its  function  of  leveling  the  income-stream  of  the 
clothier. 


244  THE  RATE  OF   INTEREST  [Chap.  XIII 

Sometimes  merchants  contract  short-time  or  periodic 
loans,  not  for  some  specific  transaction  such  as  the  purchase 
of  stock  in  trade,  but  for  general  business  purposes,  as,  for 
instance,  improvement  or  enlargement.  In  this  case,  the 
extraordinary  expense  involved  may  be  met  by  a  species 
of  loan  called  "accommodation  paper."  Evidently  its 
function  is  precisely  the  same ;  namely,  to  rectify  the  time- 
shape  of  the  income-stream.  In  Wall  Street  and  other 
speculative  centers  a  type  of  loan  known  as  the  "call  loan" 
is  common,  subject  to  redemption  at  the  pleasure  of  the 
lender,  and  used  by  the  speculator  for  the  purchase  of  se- 
curities. The  speculator  borrows  when  he  wishes  to  buy, 
and  repays  when  he  has  sold;  and  by  adroitly  arranging 
his  loans  prevents  the  sudden  draining  or  flushing  of  his 
income-stream  which  these  purchases  and  sales  would 
otherwise  involve. 

In  all  the  cases  which  have  been  described,  the  loan  grows 
out  of  a  purchase  or  group  of  purchases;  and  since  the 
tendency  of  every  purchase  is  to  decrease  one's  income,  and 
of  every  sale  to  increase  it,  it  is  clear  that  loans  contracted 
for  a  purchase  and  extinguished  by  a  sale  have  as  their 
function  the  obliteration  of  these  decreases  and  increases 
of  the  income-stream.  It  is  clear,  therefore,  that  these 
commercial  loans  fit  into  the  theory  of  interest  which  has 
been  propounded. 

§5 

The  second  class  of  business  loans  is  that  of  long-time 
loans  or  "  permanent "  investments.  In  this  class  are  placed 
mortgages,  whether  on  farms  or  on  urban  real  estate.  As 
shown  by  Mr.  George  K.  Holmes  of  the  United  States  Census, 
more  than  two  thirds  of  farm  mortgages  are  contracted  for 
the  purchase  of  the  property,  and  the  remainder  principally 
for  improving  it,  or  for  the  purchase  of  farm  implements 
and  other  durable  wealth  or  property.  These  purchases 
or  improvements,  involving  as  they  do  large  expenditures, 
would  be  difficult  or  impossible  without  loans.  If  the  attempt 


Sec.  6]        APPLICATION  TO  ACTUAL  CONDITIONS  245 

were  made  to  enter  into  them  without  recourse  to  a  loan  mar- 
ket, they  would  cause  temporary  depressions  in  the  income- 
streams  of  the  farmers.  The  farmer  who  attempted  to  buy 
his  farm  without  a  loan  would  have  to  cut  down  his  current 
expenses  to  a  minimum  and  suffer  a  corresponding  reduction 
in  his  enjoyable  income-stream,  unless  he  avoided  this  result 
by  some  other  of  the  methods  which  have  been  explained, 
such  as  "  the  method  of  buying  and  selling."  For  instance, 
he  may  sell  some  other  capital  in  order  to  buy  his  farm. 

Mortgages  on  city  lots  are  usually  for  the  purpose  of  im- 
proving the  property  by  erecting  buildings  upon  it.  Here, 
again,  the  expense  involved  would,  if  taken  out  of  income, 
reduce  the  income  of  the  owner  temporarily  to  very  small  pro- 
portions. He  naturally  prefers  to  compensate  for  such  extra- 
ordinary inroads  by  a  mortgage  which  defers  this  expense  to 
the  future,  when  his  receipts  will  be  more  adequate  to  meet  it. 

We  come  next  to  the  loans  of  business  corporations  and 
firms,  such,  for  instance,  as  railroad  bonds  and  debentures,  the 
securities  of  street  railroads,  telegraph,  and  telephone  com- 
panies, and  other  "industrials."  These  loans  are  usually 
issued  for  construction  purposes,  as  in  cases  in  which  a  rail- 
road wishes  to  extend  its  lines,  replace  iron  rails  with  steel 
ones,  or  a  curved  route  by  a  straighter  one.  The  borrowers 
in  this  case  are  the  stockholders.  They  may  be  said 
to  contract  the  loan  in  order  not  to  have  the  expenses 
of  the  improvement  taken  out  of  their  dividends.  Sometimes, 
where  the  dividends  are  large  and  the  stockholders  few,  divi- 
dends are  applied,  in  part  or  wholly,  to  the  making  of  im- 
provements. But  ordinarily  the  reduction  in  the  stockholder's 
income-stream  is  avoided  by  the  device  of  inviting  the  bond- 
holders to  cancel  the  outgoes  connected  with  the  improve- 
ment, in  consideration  of  receiving  a  part  of  the  increased 
income  which  will  later  follow  from  these  improvements. 

§6 

We  see,  therefore,  that  business  loans,  or  loans  growing 
out  of  a  purchase  and  sale,  are  as  truly  for  the  purpose  of 


246  THE  RATE  OP  INTEREST  [Chap.  XIII 

reshaping  the  income-streams  as  are  private  and  public 
loans.  The  reasons  that  business  loans  are  usually  re- 
garded by  economists  as  on  a  different  footing  from  private 
and  public  loans  appear  to  be  three :  — 

1.  The  proceeds  of  business  loans  are  usually  spent,  not 
for  the  borrower's  bread  and  butter,  but  for  durable 
capital;  consequently  the  loan  seems  not  to  be  connected 
with  income,  but  rather  with  capital.  A  spendthrift 
who  borrows  $1000  in  order  to  pay  for  wines  is  certainly 
to  be  distinguished  from  a  merchant  who  borrows  the  same 
sum  in  order  to  pay  for  new  stock  in  trade.  Yet  in  either 
case  the  loan  adds  $1000  to  immediate  income  beyond  what 
the  income  would  have  been  without  the  loan  but  with  the 
expense  for  the  wines  or  the  stock  in  trade. 

To  make  the  comparison  as  simple  as  possible,  let  us  sup- 
pose that  the  two  men  were  each  enjoying  an  income  of 
$10,000  a  year.  This  represents  the  value  of  their  nourish- 
ment, clothing,  shelter,  etc.,  which  constitute  true  income. 
In  the  year  (say  1901)  of  the  proposed  loan,  each  man  has 
two  courses  open  to  him :  (1)  he  may  meet  the  expenditure 
for  wines  or  stock  in  trade  by  sacrificing  one-tenth  of  his 
$10,000  worth  of  nourishment,  clothing,  shelter,  etc.,  or  (2) 
he  may  meet  it  by  borrowing.  If  the  spendthrift  follows  the 
first  course  and  meets  the  expenditure  by  skimping  out  of 
his  $10,000  income,  he  will  not  suffer  any  change  in  the 
value  of  his  income,  but  will  obtain  $1000  worth  of  wine 
drinking,  at  a  sacrifice  of  $1000  worth  of  other  pleasures. 
His  income  for  the  year  1901  will  still  be  $10,000.  Nor  will 
there  be  any  necessary  change  in  the  income  of  subsequent 
years.  He  merely  changes  the  composition  of  this  year's 
enjoyable  income  partly  into  wine-drinking,  but  his  income 
remains  $10,000  a  year.  The  merchant,  however,  who 
skimps  out  of  his  $10,000  income  in  1901  in  order  to  pay  for 
stock  in  trade,  will  actually  reduce  his  enjoyed  income  of 
1901  by  $1000 ;  for  this  stock  in  trade,  unlike  wine,  will 
not  give  any  immediate  satisfaction.  It  serves  only  as  a 
means  of  securing  future  satisfactions,  so  that,  let  us  say, 


Sec.  6]        APPLICATION  TO  ACTUAL  CONDITIONS 


247 


$1100  may  be  enjoyed  in  1902.  The  income  of  the  mer- 
chant will  thus  be,  not  $10,000  each  year,  as  was  that  of 
the  spendthrift,  but  $9000  in  1901  and  $11,100  in  1902. 

Having  seen  what  effect  the  expenditures  would  have  in 
the  two  cases  without  recourse  to  borrowing,  we  next  ask 
what  will  be  the  effect  in  the  two  cases  of  borrowing  $1000 
in  1901  and  repaying,  let  us  say,  $1050  in  1902.  The  spend- 
thrift who  borrows  to  get  his  $1000  worth  of  wine  will  have, 
in  1901,  that  much  more  of  enjoyed  income,  making  a  total 
enjoyed  income  in  that  year  of  $11,000,  and  in  1902,  when 
called  upon  to  pay  his  debt  of  $1050,  he  will  have  to  sacrifice 
just  so  much  out  of  his  income  of  $10,000  for  1902.  His 
resulting  enjoyed  income  will  therefore  be  in  1902  only 
$8950.  As  to  the  merchant,  he  will  be  able  to  buy  his 
stock  in  trade  in  1901  without  the  necessity  of  any  sacrifice 
out  of  his  $10,000  for  that  year,  so  that  his  income  in  1901 
will  be  $10,000.  In  the  following  year  he  will  pay  the 
$1050  for  his  loan  out  of  the  $11,100  for  1902.  (Of  the 
$11,100,  $10,000  was  the  original  income,  and  $1100  what 
we  have  assumed  to  be  the  returns  from  his  stock  in 
trade.)  He  will  thus  have  $10,050  left  as  his  real  income 
for  that  year. 

Comparisons  are  shown  in  the  following  tables :  — 

INCOME    OF    SPENDTHRIFT 
WHO    BUYS   $1000    WORTH    OF   WINE 


1901 

1902 

Without  loan 

With  loan 

$10,000 
11,000 

$10,000 
8,950 

WHO    BUYS 

INCOME    OF 
$1000    WORTH 

MERCHANT 
OF    STOCK    IN 

TRADE 

1901 

1902 

Without  loan 

With  loan 

$  9,000 
10,000 

$11,100 
10,050 

248  THE  RATE   OF  INTEREST  [Chap.  XIII 

It  is  clear  that  in  each  case  the  effect  of  the  loan  is  to  add 
$1000  to  the  income  of  1901  and  subtract  $1050  from  that 
of  1902.  There  is  absolutely  no  difference  between  the 
two  men  in  this  respect.  The  difference  between  them  is 
chiefly  that  the  spendthrift  is  making  a  foolish  and  the 
merchant  a  wise  addition  to  his  income  of  1901  at  the 
expense  of  that  of  the  year  following,  and  this  difference  is 
only  one  of  degree,  due  to  the  fact  that  the  final  satis- 
factions by  means  of  the  wine  come  earlier  than  the 
satisfactions  obtained  by  means  of  the  stock  in  trade. 

2.  But  the  example  given  of  the  "consumption "-loan  is 
not  the  only  one  possible,  and  no  doubt  it  will  still  seem  to 
some  readers  that  there  must  be  another  difference  between 
production-  and  consumption-loans.  Suppose  the  case  of  a 
victim  of  misfortune,  such  as  illness.  To  tide  him  over  his 
emergencies  he  is  compelled  to  borrow,  using  the  proceeds 
of  his  loan  merely  to  meet  his  grocer's  and  butcher's  bills. 
Here  is  indeed  a  case  of  a  "  consumption  "-loan  which  is  not 
foolish,  and  yet  is  surely  different  from  the  loan  of  the  mer- 
chant to  buy  stock  in  trade. 

The  effect  of  business  loans  is  to  enable  a  merchant  to 
embark  on  an  enterprise,  while  personal  loans  merely  relieve 
needs.  Let  us  examine  this  difference.  It  is  not  a  dif- 
ference which  invalidates  the  principle  that  both  loans  are 
additions  to  present  income  at  the  expense  of  future  income. 
The  unfortunate,  with  his  misfortune,  but  without  his  loan, 
would  have,  let  us  say,  an  income  of  $9,000  in  1901  and 
$11,100  in  1902,  which  are  the  same  figures  we  assumed 
for  the  merchant  with  his  investment  but  without  his  loan. 
With  the  loan,  therefore,  the  unfortunate  and  the  merchant 
would  be  in  the  same  situation.  Both  would  have  $10,000 
in  1901  and  $10,050  in  1902.  The  effect  of  the  loan  in  the 
two  cases  is  thus  identical  so  far  as  their  income-streams 
are  concerned.  The  difference  is  that  the  unfortunate, 
if  deprived  of  his  loan,  could  not  escape  from  his  income- 
stream  of  $9,000  in  1901  and  $11,100  in  1902,  whereas  the 
merchant,  if  deprived  of  his  loan,  could,  if  he  chose,  give 


Sec.  6]        APPLICATION  TO  ACTUAL  CONDITIONS 


249 


up  the  investment  in  new  stock  altogether.  If  the  merchant 
did  not  have  this  option,  the  two  cases  would  be  so  similar 
that  not  even  a  stickler  for  the  distinction  between  con- 
sumption-loan and  productive-loan  would  assert  any  es- 
sential difference.  For,  suppose  the  merchant  has  already 
been  committed,  sometime  previously,  to  buy  the  goods  for 
his  stock  in  trade,  not,  perhaps,  realizing  that  he  would  be 
unable  to  pay  for  them  without  borrowing  or  skimping. 
When  the  time  arrives  that  he  must  of  necessity  buy  the 
goods  and  pay  for  them,  he  finds  that  a  loan  is  badly  needed 
to  avoid  pinching  himself  in  income.  He  will  now  think 
of  the  loan,  not  as  enabling  him  to  buy  stock  in  trade,  for 
that  must  be  done  anyway,  but  as  enabling  him  to  buy  his 
bread  and  butter.  In  short,  his  loan,  like  the  unfortunate's, 
is  a  necessity-loan.  It  is  because  ordinarily  the  merchant 
is  not  thus  constrained  to  buy  the  goods  that  the  loan  is 
connected,  in  his  mind,  with  their  purchase  rather  than 
with  his  private  necessities.  It  still  serves  to  relieve 
that  income,  but  he  has  another  method  of  relief,  —  not 
to  buy  the  goods  at  all.  The  contrast,  then,  between 
him  and  the  unfortunate  is  simply  that  he  has  a  third 
possible  course  which  the  latter  does  not  have.  This  is 
shown  in  the  following  tables :  — 

INCOME  OF  MERCHANT 


1901 


1902 


A  Without  loan  and  without  investment 
B  Without  loan  but  with  investment    . 
C  With  loan  and  with  investment    .     . 


$10,000 

9,000 

10,000 


S10,000 
11,100 
10,050 


INCOME  OF  UNFORTUNATE 


1901 

1902 

B  Without  loan 

$  9,000 
10,000 

$11,100 

C  With  loan 

10,050 

250  THE  RATE  OF  INTEREST  [Chap.  XIII 

We  see  here  that  the  unfortunate  has  two  options,  B  and 
C,  and  the  merchant  three  possible  options,  A,  B,  and  C. 
It  is  the  existence  of  this  third  option  A  which  makes  the 
chief  real  difference  between  the  merchant  borrower  and  the 
borrower  in  misfortune.  So  far  as  the  other  two  options  are 
concerned,  the  two  men  are  similarly  situated.  That  this 
fact  is  overlooked  is  due  to  the  unconscious  substitution, 
in  considering  the  case  of  the  merchant,  of  the  third  option, 
A,  for  the  second,  B.  That  is  to  say,  when  the  effect  of 
a  merchant's  loan  is  considered,  this  effect  is  measured 
with  reference  to  his  situation  without  the  loan  and 
without  the  purchase  of  the  goods,  instead  of  with  reference 
to  hfs  situation  without  the  loan  but  urith  the  purchase. 
The  latter  method  measures  the  effect  of  the  loan  in  the 
sense  that  it  shows  the  difference  produced  by  its  pres- 
ence or  absence,  other  things  being  equal.  It  treats  the 
merchant's  loan  in  the  same  way  that  the  unfortunate's 
loan  is  treated,  and  thus  puts  the  two  on  the  same 
basis.  The  true  sequence  of  thought  then  is:  Of  the 
two  options  A  and  B,  the  merchant  selects  B  (buying 
the  goods)  because  it  has  the  greater  present  value  (or,  what 
amounts  to  the  same  thing,  because  the  rate,  10  per  cent., 
of  the  return  of  $1100  on  the  sacrifice  of  $1000  is  greater 
than  the  rate  of  interest,  5  per  cent.) ;  then  he  selects  C 
(borrowing  money),  which  has  the  same  present  value 
as  B,  but  a  more  desirable  time-shape.  This  description 
takes  account  of  the  whole  series  of  operations,  and  cor- 
responds to  the  principles  propounded  in  Chapter  VIII. 

3.  It  is  the  third  option  A  which  gives  rise  to  the  con- 
tention that  the  loan  produces  a  profit  not  possible  or  easy 
without  it,  and  that  it  is,  therefore,  "  productive."  We  have 
just  seen  that  the  loan  phenomena  are  resolved  into  two 
separate  steps,  the  rejection  of  A  in  favor  of  B,  and  the 
rejection  of  B  in  favor  of  C.  Yet  since  it  may  often  happen, 
as  shown  in  Chapter  VIII,  that  the  first  step  (choice  of 
options)  would  not  be  taken  unless  the  second  step  (loan) 
were  already  in  contemplation,  it  is  true  that,  in  a  sense, 


Sec.  7]        APPLICATION  TO  ACTUAL  CONDITIONS  251 

the  choice  of  the  loan  includes  the  choice  between  the 
options  A  and  B.  Looked  at  in  this  way,  the  effect  of 
the  loan  is  measurable  by  comparing  C  with  A,  such  com- 
parison including  both  the  steps  stated.  In  this  sense, 
and  in  this  sense  alone,  is  the  loan  "productive."  It  is 
productive  in  that  it  enables  the  merchant  to  buy  the 
goods.  He  thus  chooses  an  option  (B)  which  has  an 
advantage  (over  ^)  in  present  value,  or  yields  a  rate  of 
return  on  sacrifice  (10  per  cent.)  greater  than  the  rate 
of  interest.  The  reason  that  the  loan  is  regarded  as 
"productive,"  then,  is  that  it  gives  the  merchant  the  op- 
portunity to  make  10  per  cent,  instead  of  5  per  cent.  But 
obviously  it  is  not  the  loan  (choice  of  C  rather  than  B) 
which  yields  the  10  per  cent. ,  but  the  choice  of  options  with- 
out the  loan  (B  rather  than  A).  The  profit  is  the  advantage 
of  B  over  A ;  but  the  loan  merely  substitutes  C  as  a  more 
desirable  equivalent  of  5.  It  does  not  add  to  the  profit, 
though  it  changes  the  form  in  which  it  appears.  After  the 
loan,  the  profit  appears  in  the  accounts  for  1902  in  the 
form  of  $50  more  income  for  C  than  for  A. 

If,  after  all  has  been  said  and  understood,  any  one  still 
prefers  to  call  such  a  loan  "productive,"  no  objection  is 
offered,  provided  always  that  it  is  made  wholly  clear 
what  is  meant  by  the  term  "  productive."  The  essential 
point  is  that  our  theory  of  interest  is  not  restricted  in 
its  application  to  personal  and  public  loans,  but  includes 
the  loans  of  business.  These  business  loans  come  into 
the  same  theory  as  the  other  loans,  and  differ  only  in 
the  existence  of  a  wider  range  of  choice  in  income- 
streams. 

§7 

We  have  seen  that  the  theory  of  interest  which  has  been 
propounded  is  adequate  to  explain  the  motives  which  lead 
to  borrowing  and  lending  in  the  actual  business  world. 
The  purpose  of  loans  in  all  cases  may  be  said  to  be  to  modify 
the  shape  of  income-streams  so  as  to  suit  the  particular 


252  THE  RATE  OF  INTEREST  [Chap.  XIII 

requirements  of  the  case,  —  to  increase  present  income  at 
the  sacrifice  of  future,  and  to  eke  out  present  scarcity 
in  anticipation  of  future  abundance.  As  Jevons  stated, 
capital  is  required  to  enable  one  to  support  himself  while 
engaged  in  undertakings  which  require  time. 

Tlie  foregoing  classification  is  made  from  the  standpoint 
of  the  borrower.  From  the  standpoint  of  the  lender,  loans 
do  not  need  to  be  so  minutely  classified.  The  lender  is 
usually  either  one  who  wishes  to  invest  permanently,  or  one 
who  wishes  to  invest  temporarily.  The  former  may  lend 
on  mortgage,  or  he  may  buy  the  securities  of  companies, 
governments,  or  municipalities,  or  he  maybe  a  depositor  in  a 
savings  bank.  In  all  cases  the  lender  is  evidently  sacrificing 
what  he  might  enjoy  in  present  income,  in  order  that  he  may 
have  a  still  larger  income  in  the  future.  In  other  words,  he 
is  modifying  the  time-shape  of  his  income  curve  in  a  manner 
opposite  to  that  which  the  borrower  pursues.  When  he 
invests  for  short  times,  this  course  is  generally  due  to  a 
periodic  fluctuation  in  his  income-stream,  the  large  present 
flow  being  precedent  to  a  shortage  in  the  not  far  distant 
future.  Business  men  and  institutions  are  in  this  way 
constantly  investing  for  short  periods  funds  which  otherwise 
would  exist  in  the  form  of  idle  cash.  The  government 
or  individual  which  we  supposed  to  have  borrowed  at  the 
time  of  deficit  in  anticipation  of  surplus  may,  instead,  fol- 
low the  reverse  policy  of  investing  the  surplus  at  interest, 
in  order  to  provide  better  for  the  payment  of  expenses  at  the 
time  of  anticipated  deficit. 

§  8 

The  same  person  may  be  alternately  borrower  and  lender, 
according  to  the  exigencies  of  his  income-stream.  When  the 
same  person  is  simultaneously  borrower  and  lender,  he  be- 
comes a  broker  for  managing  credit  operations  for  other 
persons.  This  is  usually  the  function  of  institutions  such 
as  banks  of  discount  and  deposit,  savings  banks,  trust  com- 
panies, exchange  brokerage  firms,  and  mortgage  companies. 


Sec.  8]         APPLICATION  TO   ACTUAL  CONDITIONS  253 

It  is  through  such  firms  that  borrowers  and  lenders  usually 
reach  each  other,  rather  than  directly ;  but  whether  directly 
or  by  means  of  such  intermediaries,  the  borrowers  and 
lenders  are  constantly  playing  into  each  other's  hands. 
This  is  particularly  evident  in  the  case  of  periodic  fluctua- 
tions ;  for  it  usually  happens  that  the  same  cycle  of  opera- 
tions which  makes  one  man's  income  alternately  large  and 
small  will  make  another  man's  alternately  small  and  large. 
Thus,  when  the  clothing  manufacturer  sells  to  the  retailer 
of  ready-made  clothing,  not  only  does  this  operation  tend 
to  make  inroads  in  the  income-stream  of  the  latter,  but  it 
also  tends  to  bring  to  the  former  an  accession  of  income 
inconveniently  concentrated.  For  this  reason  the  manu- 
facturer may  decide  to  keep  the  commercial  note  which  the 
clothier  makes  to  him,  rather  than  to  discount  it  at  a  bank. 
The  manner  in  which  fluctuations  in  income-streams 
mutually  compensate  among  borrowers  and  lenders  is  well 
seen  in  the  South,  where  cotton  planters  have  long  been 
accustomed  to  borrow  of  the  banks  in  springtime,  to  repay 
in  the  fall  after  the  cotton  is  sold.  Until  recently  the  banks 
which  supplied  these  loans  found  difficulty  in  leveling  the 
consequent  irregularities  produced  in  their  own  income- 
streams.  They  were  forced  to  do  so  largely  by  keeping  an 
idle  stock  of  cash,  or  investing  it  at  low  rates  in  Northern 
banks.  But  recently  cotton  mills  have  settled  in  the  South, 
with  a  cycle  of  income  exactly  the  reverse  of  that  of  the 
planters.  They  buy  their  crops  in  the  fall,  manufacture 
through  the  winter,  and  sell  in  the  spring.  The  conse- 
quence is  that  they  come  to  the  banks  for  loans  in  the  fall, 
which  is  just  the  time  when  the  banks  are  receiving  their 
pay  from  the  planters,  and  liquidate  these  loans  in  the 
spring,  at  just  the  time  when  the  banks  are  in  need  of 
funds  to  lend  to  the  planters.  In  this  way  the  irregularities 
in  the  income-streams  of  both  planters  and  manufacturers 
are  leveled,  virtually  by  mutual  cancellation,  but  actually 
through  the  intermediation  of  the  banks. 


254  THE  RATE  OF  INTEREST  [Chap.  XIII 

§  9 

Hitherto  we  have  considered  loans  only  with  reference  to 
the  time  of  issue  and  repayment.  But  it  frequently  happens 
that  loans  are  transferred  at  points  intermediate  between 
these  two  dates.  In  that  case  they  pass  by  sale  like  other 
property,  and  affect  the  income-streams  of  those  who  buy  and 
sell  in  precisely  the  same  way  as  if  they  lent  and  borrowed. 
The  buyer  of  a  security  is  in  the  same  position  as  a  lender, 
—  he  parts  with  present  income  for  the  sake  of  future. 
The  seller  of  a  loan  security  is  in  the  same  position  as  a 
borrower,  —  he  is  securing  present  income  and  foregoing 
the  future  interest  he  would  otherwise  receive.  The  price 
at  which  such  loan  securities  are  sold  will  determine  the 
rate  of  interest  realized  and  borne  by  the  buyer  and  seller 
respectively.  The  effects  caused  by  the  transfer  of  loans 
may  be  negatived  by  later  transactions.  The  seller  of  a 
bond  may  not  really  use  the  proceeds  to  swell  a  large  income, 
but  may  reinvest  in  some  other  security,  and  the  buyer  may 
not  hold  the  security  until  maturity,  but  may  sell  again 
at  the  next  turn  of  the  market. 

What  has  been  said  of  loan  securities  applies  also  to  every 
form  of  property  which  may  be  regarded  in  the  same  light. 
The  buyer  of  railway  stock  is  not  very  different  from  the 
buyer  of  railway  bonds,  or  the  lender.  He  also  is  sacri- 
ficing present  income  for  future,  so  far  as  this  particular 
purchase  is  concerned,  even  though,  as  just  shown, 
the  effect  may  be  negatived  by  some  other  transaction. 
Likewise  the  seller  of  railroad  stock  is  similar  to  the  seller  of 
bonds,  or  the  borrower.  The  only  distinction  is  that  in 
the  case  of  buying  and  selling  stock  the  rate  of  interest 
is  implicit  rather  than  explicit. 

§10 

Explicit  and  implicit  interest  really  differ,  however, 
in  degree  rather  than  in  kind.     An  income  bond,  while 


Sec.  10]      APPLICATION  TO   ACTUAL  CONDITIONS  255 

nominally  yielding  explicit  interest,  may  actually,  if  the 
income  is  inadequate,  yield  quite  a  different  interest,  and 
the  price  of  sale  takes  into  account  the  latter  contingency 
quite  as  much  as  the  former.  Preferred  stock,  likewise, 
while  nominally  involving  the  risk  of  non-payment,  often 
represents  a  case  more  nearly  like  that  of  explicit  interest. 
It  is  quite  as  possible,  on  the  basis  of  the  purchase  price 
and  the  practical  certainty  of  a  definite  fixed  income,  to 
calculate  the  rate  of  interest  to  be  realized  to  the  investor, 
as  in  the  case  of  the  bond  buyer.  In  the  case  of  ordinary 
stock,  however,  in  order  to  calculate  the  interest  to  be 
realized,  it  becomes  necessary  to  make  a  forecast  of  the 
probable  dividends.  It  is  where  the  element  of  chance  thus 
enters  that  implicit  interest  really  differs  from  explicit. 
Where  the  ownership  of  an  article  of  wealth  is  total  instead 
of  partial,  the  element  of  chance  is  always  present.  In  fact, 
bonds,  so  far  as  they  escape  from  the  universal  reign  of 
chance,  do  so  only  by  carving  out  of  the  fluctuating  income 
arising  from  a  mass  of  capital-wealth  a  certain  definite  part, 
small  enough  not  to  absorb  the  whole  even  at  its  lowest 
ebb.  But  while  the  rate  of  interest  is  somewhat  difficult 
to  calculate  in  advance  in  the  case  of  other  property  than 
loan  securities,  it  may  be  approximately  estimated,  and 
from  the  rate  which  has  been  actually  realized  in  the  past 
it  may  sometimes  even  be  exactly  calculated.  In  the  case 
of  land,  it  is  not  uncommon  to  reckon  the  value  of  so  many 
years'  purchase  of  the  crop  returns,  on  the  assumption  that 
the  same  value  of  the  crop  returns  will  continue  indefinitely. 
The  element  of  risk,  which  is  so  dominant  in  actual 
business  relations,  has  also  been  considered  in  the  theory  of 
this  book.  The  buying  and  selling  of  property  serve  to 
modify  not  only  the  time-shape  of  the  income-stream,  but 
also  the  degree  of  certainty.  The  investor  who  wishes  to 
take  chances  may  invest  in  stock,  and  he  who  does  not, 
in  bonds.  Risk  constitutes  the  real  difference  between 
them,  and  the  reason  for  the  existence  of  the  two  types 
of  securities.     Both  are  investors,  and  both  sacrifice  present 


256  THE  RATE  OF  INTEREST  [Chap.  XIII 

income  for  future;  but  one  assumes  a  future  income  with 
risk  and  the  other  receives  one  without  risk,  or  at  any 
rate,  with  no  large  degree  of  risk.  That  stockholders  and 
bondholders  are  both  investors  is  not  inconsistent  with  the 
fact  already  emphasized  that  the  stockholder  is  a  borrower 
of  the  bondholder  as  a  lender.  In  dealing  with  each  other 
they  are  on  opposite  sides  of  the  market,  the  bondholder 
being  a  buyer  or  investor  and  the  stockholder  a  seller  or 
borrower.  But  in  dealing  with  "  the  company,"  they  are 
on  the  same  side  of  the  market  ;  both  are  buyers  of 
securities,  or  investors. 

Thus  by  borrowing  and  lending,  or  by  buying  and  selling, 
an  individual  regulates  the  character  of  his  income- stream 
to  suit  his  individual  needs  and  idiosyncrasies.  This  ad- 
justment involves  comparisons  of  risk  and  of  futurity, 
and  in  the  latter  case  involves  a  rate  of  interest,  implicit 
or  explicit.  This  rate  is  utilized  by  individuals  to  enable 
them  to  increase  or  decrease  the  flow  of  their  income  at 
different  periods  of  time,  and  it  is  through  their  efforts  to 
do  so,  by  bargaining  with  each  other,  that  the  rate  of 
interest  is  itself  determined.  The  theory  of  its  determina- 
tion applies  to  the  actual  loans  of  business,  loans  of  neces- 
sity, improvidence,  or  purchase,  loans  of  persons,  corpora- 
tions, and  loan  brokers,  and  applies  also  to  cases  in  which 
there  are  no  contract  loans  at  all,  but  only  the  buying, 
selling,  and  valuing  of  property,  in  which  transactions  the 
rate  of  interest  is  always  implicitly  contained. 


CHAPTER   XIV 

INDUCTIVE   VERIFICATION    (MONETARY) 
§    1 

No  study  of  the  principles  governing  the  rate  of  interest 
would  be  complete  without  verification  by  facts.  In  this 
chapter  those  facts  will  be  presented  which  bear  on  the 
problem  discussed  in  Chapter  V,  the  problem  of  apprecia- 
tion and  interest.  The  object  will  be  to  ascertain  the 
extent  to  which,  in  the  actual  world,  the  appreciation  or 
depreciation  of  the  monetary  standard  is  foreseen  by  bor- 
rowers and  lenders,  and  provided  for  in  the  rates  of  interest 
upon  which  they  agree. 

At  the  outset  the  question  arises,  Plow  can  a  merchant 
be  said  to  foresee  the  appreciation  of  money  ?  Appreciation 
is  a  subtle  concept.  Few  business  men  have  any  clear 
ideas  about  it.  Economists  disagree  as  to  its  definition, 
and  statisticians  as  to  its  measurement.  If  we  ask  a 
merchant  whether  or  not  he  takes  account  of  appreciation, 
he  will  say  that  he  never  thinks  of  it,  that  he  always 
"regards  a  dollar  as  a  dollar."  In  his  mind,  other 
things  maj'^  change  in  terms  of  money,  but  money  itself 
does  not  change.  Yet  it  may  be  true  that  he  does 
take  account  of  a  change  in  the  purchasing  power  of 
money,  under  guise  of  a  change  in  the  prices  of  other 
things.  In  our  daily  life  we  seldom  think  of  the  earth 
as  moving;  nevertheless  we  take  account  of  its  rotation 
whenever  we  speak  of  "sunrise"  or  "sunset."  During 
a  period  of  paper-money  inflation  the  ordinary  man 
conceives  the  premium  on  gold  as  a  rise  of  gold  bullion, 
not  a  fall  of  the  paper  money;  but  he  arrives  at  the 
same  practical  results.  Appreciation  of  money,  whether 
in  reference  to  gold  bullion,  commodities,  or  labor,  is  in 
effect  taken  account  of  in  the  practical  man's  forecast  of 

s  257 


258  THE  RATE   OF  INTEREST  [Chap.  XIV 

all  the  economic  elements  which  concern  him,  —  the  prices 
of  his  product,  the  cost  of  his  living,  the  wages  of  his  work- 
men, and  so  forth.  Moreover,  he  takes  account  of  the 
relative  importance  of  these  factors  as  affecting  himself, 
and  not  of  their  relative  importance  in  the  elaborate  aver- 
ages of  the  statistician,  —  averages  which  may  emphasize 
some  particular  commodity  or  labor  whose  fluctuations 
have  no  interest  for  him.  His  own  aim  is  not  to  predict 
the  index  numbers  of  Sauerbeck  or  of  the  United  States 
Bureau  of  Labor,  but  to  foresee  those  price  changes  which 
affect  his  own  economic  future.  To  foresee  a  rise  or  fall  of 
a  particular  price  is  to  that  extent  to  foresee  a  change  in 
the  purchasing  power  of  money.  Such  forecasts  enable  a 
man  to  make  reasonably  correct  decisions,  and  in  particu- 
lar to  contract  a  loan  with  intelligence.  If  gold  appreciates 
in  such  a  way  or  in  such  a  sense  that  he  expects  for  himself 
a  shrinking  margin  of  profit,  he  will  be  cautious  about  bor- 
rowing unless  interest  falls ;  and  this  ver}''  unwillingness  to 
borrow,  lessening  the  demand  in  the  ''money  market,"  will 
bring  interest  down.  On  the  other  hand,  if  inflation  is 
going  on,  he  will  see  rising  prices  and  rising  profits,  and 
will  be  stimulated  to  borrow  capital  unless  interest  rises; 
moreover,  this  willingness  to  borrow  will  itself  raise  interest. 
Foresight  is  clearer  and  more  prevalent  to-day  than 
ever  before.  Multitudes  of  trade  journals  and  investors' 
reviews  have  their  chief  reason  for  existence  in  supplying 
data  on  which  to  base  prediction.  Every  chance  for  gain 
is  eagerly  watched  for.  An  active  and  keen  speculation  is 
constantly  going  on  which,  so  far  as  it  does  not  consist 
of  fictitious  and  gambling  transactions,  performs  a  well- 
known  and  provident  function  for  society.  Is  it  reasonable 
to  believe  that  foresight,  which  is  the  general  rule,  has  an 
exception  as  applied  to  falling  or  rising  prices  ? 

§  2 

Appreciation  and  depreciation  in  this  book  are  used  in 
a  purely  relative  sense.     If  gold  appreciates  relatively  to 


Sec.  2]      INDUCTIVE  VERIFICATION  (MONETARY)  259 

silver,  then  necessarily  silver  depreciates  relatively  to  gold. 
Any  standard  appreciates  1  per  cent,  relatively  to  another 
standard  if  a  certain  amount  of  it  now  commands  101 
units  in  this  other  standard,  when  previously  it  commanded 
only  100  units. 

General  evidence  that  an  expected  appreciation  or  de- 
preciation of  money  has  an  effect  on  the  rate  of  interest  in 
that  money  can  be  obtained  from  several  sources.  During 
the  free-silver  agitation  of  1895-6,  it  was  observed  that 
municipalities  could  often  sell  gold  bonds  at  better  terms 
than  "currency"  or  "coin"  bonds.  There  was  a  strong 
desire  on  the  part  of  lenders  to  insert  a  gold  clause  in 
their  contracts,  and  they  were  willing  to  yield  something 
in  their  interest  to  secure  it.  The  same  tendency  was 
strikingly  shown  in  California '  during  the  inflation  period 
of  the  Civil  War.  For  a  time,  gold  contracts  could  not  be 
enforced,  and  in  consequence  interest  rates  were  excep- 
tionally high. 

During  a  period  of  progressive  paper  inflation  the  rate 
of  interest  in  contracts  drawn  on  a  paper  basis  is  high. 
This  was  true  during  the  Civil  War,  and  also  during  the 
currency  troubles  in  the  thirties.  Raguet  wrote : ^  "In 
the  six  months  before  the  suspension  of  '37,  although  the 
amount  of  the  currency  was  greater  than  it  had  ever  been 
before  in  the  United  States,  yet  the  scarcity  of  money  was 
so  great  that  it  commanded  from  1  per  cent,  to  3  per  cent, 
per  month."  It  would  be  unsafe  to  found  much  inference 
on  these  facts ;  their  significance  may  be  partly  or  whoUy 
different.  But  they  raise  a  presumption  that  anticipation 
of  further  depreciation  of  currency  tends  to  increase  the 
rate  of  interest. 

A  definite  test  must  be  sought  where  two  standards  are 
simultaneously  used.     An  excellent  case  of  this  kind  is 

»  Bernard  Moses,  "Legal  Tender  Notes  in  California,"  Quarterly 
Journal  of  Economics,  October,  1892,  p.  15. 

^  Currency  and  Banking  (1839),  p.  139;  also  Sumner,  History  of 
Banking,  New  York  (1896),  p.  264. 


260 


THE  RATE  OF  INTEREST 


[Chap.  XIV 


supplied  by  two  kinds  of  United  States  bonds,  one  payable 
in  coin  and  the  other  in  currency.  From  the  prices  which 
these  bonds  have  fetched  in  the  market  it  is  possible  to 
calculate  the  interest  realized  to  the  investor.  The  cur- 
rency bonds  were  known  as  currency  sixes  and  matured  in 
1898  and  1899.  The  coin  bonds  selected  for  comparison 
were  the  fours  of  1907.  The  following  table  gives  the  rates 
of  interest  realized  in  the  two  standards,  together  with  the 
premium  on  gold. 


RATES   OF   INTEREST   REALIZED   FROM   DATES    MEN- 
TIONED   TO    MATURITY  1 


Coin 

Cur- 
rency 

Price  of  Gold 

Coin 

CUR- 
RENCT 

Jan.,  1870 

6.4 

5.4 

119.9 

Jan.,  1879 

3.7 

4.5 

July 

1870 

5.8 

5.1 

112.2 

Jan.,  1880 

3.8 

4.0 

Jan., 

1871 

6.0 

5.3 

110.8 

Jan.,  1881 

3.3 

3.4 

July 

1871 

5.8 

5.0 

113.2 

Jan.,  1882 

3.0 

3.5 

Jan., 

1872 

5.3 

4.9 

109.5 

Jan.,  1883 

2.9 

3.3 

July 

1872 

5.6 

5.0 

113.9 

Jan.,  1884 

2.6 

2.9 

Jan., 

1873 

5.7 

5.1 

111.9 

May,  1885 

2.7 

2.7 

July 

1873 

5.4 

5.0 

115.3 

Jan.,  1886 

2.6 

2.6 

Jan., 

1874 

5.0 

5.0 

110.3 

Jan.,  1887 

2.3 

2.6 

July 

1874 

5.1 

4.9 

110.7 

Mar.,  1888 

2.3 

2.9 

Jan., 

1875 

5.0 

4.7 

112.6 

Jan.,  1889 

2.2 

2.6 

July 

1875 

5.1 

4.4 

117.0 

May,  1890 

2.1 

2.6 

Jan. 

1876 

4.7 

4.4 

112.9 

July,  1891 

2.4 

3.0 

July 

,  1876 

4.5 

4.2 

112.3 

Jan.,  1892 

2.6 

3.1 

Jan. 

1877 

4.5 

4.4 

107.0 

Mar.,  1893 

2.8 

3.1 

July 

,  1877 

4.4 

4.3 

105.4 

Nov.,  1894 

2.7 

3.5 

Jan. 

1878 

5.0 

4.6 

102.8 

Aug.,  1895 

2.8 

3.6 

July 

,  1878 

3.9 

4.4 

100.7 

Aug.,  1896 

3.2 

4.3 

*  This  table  has  been  obtained  by  the  aid  of  the  usual  brokers' 
bond  tables.  In  the  case  of  currency  bonds,  it  was  only  necessary 
to  deduct  accrued  interest  (if  any)  from  the  quoted  price  and  look 
in  the  table  for  the  interest  which  corresponds  to  the  price  so  found 
and  the  number  of  years  to  maturity.     In  the  case  of  coin  bonds, 


Sec.  3]       INDUCTIVE  VERIFICATION   (MONETARY)  261 

Several  points  in  this  table  deserve  notice.  In  1870 
the  investor  made  6.4  per  cent,  in  gold  but  was  willing  to 
accept  a  return  of  only  5.4  per  cent,  in  currency.  This  fact 
becomes  intelligible  in  the  light  of  the  theory  which  has  been 
explained.  It  meant  the  hope  of  resumption.  Because 
paper  was  so  depreciated  there  was  a  prospect  of  a  great 
rise  in  its  value.  It  was  not  until  1878,  when  the  prospect 
of  a  further  rise  disappeared,  that  the  relative  position  of 
the  two  rates  of  interest  was  reversed.  After  resumption 
in  1879  the  two  remained  very  nearly  equal  for  several  years, 
until  fears  of  inflation  again  produced  a  divergence.  The 
quotations  for  1894,  1895,  and  1896  show  a  considerably 
higher  rate  of  interest  in  the  currency  standard  than  in  the 
coin  standard,  as  well  as  a  higher  rate  in  both  standards 
than  in  previous  years.  The  difference  is  between  2.7 
per  cent,  and  3.5  per  cent,  in  1894,  and  between  3.2  per  cent, 
and  4.3  per  cent,  in  1896.  Both  the  increase  and  the  wedg- 
ing apart  of  the  two  rates  are  explainable  as  effects  of  the 
free-silver  proposal  and  its  incorporation  (July,  1896)  in 
the  platform  of  the  Democratic  party. 


§  3 

We  see,  therefore,  that  the  facts  agree  with  the  theory 
previously  laid  down.  But  it  is  necessary  further  to  inquire 
how  close  is  this  agreement.  For  this  purpose  the  figures 
just  given  are  of  little  value.  They  represent  the  rates  of 
interest  realized  for  the  periods  between  the  dates  named 
and  the  times  at  which  the  bonds  matured;   but  as  these 

since  the  quotations  are  given  in  currency,  it  is  necessary  to  divide 
the  quoted  price  by  the  price  of  gold  in  order  to  obtain  their  price 
in  gold  {i.e.  "coin"),  and  then  proceed  as  above  indicated.  The 
quotations  of  prices  of  bonds  and  gold  are  the  "opening"  prices  for 
the  months  named,  and  are  taken  from  the  Financial  Review  (Annual 
Summary  of  the  Commercial  and  Financial  Chronicle),  1895,  The 
Commercial  and  Financial  Chronicle,  the  (New  York)  Bankers'  Maga- 
zine, and  the  Bankers'  Almanac.  After  1884,  January  quotations 
were  not  always  available. 


262 


THE  RATE   OF   INTEREST 


[Chap.  XIV 


periods  are  not  the  same  for  the  two  bonds,  the  two  cor- 
responding series  of  interest  rates  are  not  entirely  com- 
parable. Such  a  rate  of  interest  is  a  sort  of  average  of  the 
rates  of  interest  for  the  individual  years  of  the  periods  in 
question.^  Thus,  in  the  foregoing  table,  the  rate  of  interest 
in  currency  placed  opposite  January,  1870,  is  5.4  per  cent. 
This  is  the  rate  realized  between  1870  and  1899.  It  is  a 
sort  of  average  of,  say,  the  rate  of  interest  for  the  period 

RATES   OF    INTEREST   REALIZED    FROM    DATES    MEN- 
TIONED TO  JANUARY  1,  1879  (DATE  OF  RESUMPTION)  2 


Coin 

y 

Currency 
i 

Appreciation  of  Currenct 
IN  Gold 

"Expected" 
a 

Actual 

Jan.,  1870     .      . 

7.1 

6.3 

.8 

2.1 

July 

,  1870 

6.2 

5.7 

.5 

1.4 

Jan. 

1871 

6.7 

6.3 

.4 

1.3 

July 

1871 

6.4 

5.7 

.7 

1.8 

Jan. 

1872 

5.9 

5.7 

.2 

1.3 

July 

1872 

6.2 

5.7 

.5 

2.1 

Jan., 

1873 

6.5 

6.2 

.3 

2.0 

July 

1873 

6.2 

6.0 

.2 

2.8 

Jan. 

1874 

5.6 

6.1 

-.5 

2.1 

July 

1874 

5.7 

5.8 

-.1 

2.4 

Jan., 

1875 

6.0 

5.4 

.6 

3.1 

July 

1875 

6.1 

4.2 

1.9 

4.9 

Jan., 

1876 

5.4 

4.1 

1.3 

4.3 

July 

1876 

5.2 

2.4 

2.8 

4.9 

Jan., 

1877 

5.5 

4.0 

1.5 

3.5 

July 

1877 

5.7 

3.1 

2.6 

3.6 

Jan., 

1878 

8.2 

6.0 

2.2 

2.8 

July 

1878 

4.8 

2.6 

2.2 

1.4 

*  For  the  nature  of  this  average,  see  The  Nature  of  Capital  and 
Income,  Appendix  to  Chap.  XII,  §  5. 

^  Since  the  figures  in  this  table  represent  the  rates  of  interest 
which  will  render  the  "present  value,"  at  the  date  of  purchase,  of 
all  the  future  benefits  up  to  January,  1879,  equal  to  the  purchase  price, 
they  can  be  calculated  by  Horner's  method  as  indicated  in   §  9 


Sec.  3]      INDUCTIVE  VERIFICATION  (MONETARY)  263 

between  1870  and  1879  (which,  as  we  shall  see,  was  6.3 
per  cent.)  and  that  for  the  period  between  1879  and  1899 
(which was  4.5  percent.).  For  a  true  comparison  between 
coin  and  currency  rates,  we  must  seek  rates  relating  to  the 
same  period  in  each  case.  This  is  the  method  in  the  fol- 
lowing table.  In  it,  the  periods  selected  all  terminate  on 
January  1, 1879,  the  date  of  resumption  of  specie  payments. 
The  rates  of  interest  in  this  table  are  the  rates  which 
would  be  realized  by  investors  who  should  buy  the  bonds 
at  the  dates  mentioned  and  sell  them  on  January  1,  1879. 

of  the  Appendix  to  Chap.  V.  But  the  method  which  has  been  adopted 
is  less  laborious,  as  it  enables  us  to  use  the  bond  tables.  It  can  best 
be  explained  by  an  example.  The  opening  price,  January,  1870,  of 
currency  sixes  was  109i,  and  iri  January,  1879,  the  price  was  119^. 
These  prices  require  no  correction  for  accrued  interest.  Our  problem 
is,  if  a  man  spends  $109i  in  1870  and  receives  $119^  in  1879  with 
$6  per  annum  (semiannually)  in  the  meantime,  what  rate  of  interest 
does  he  realize?  Now  it  is  clear  that  the  answer  is  the  same  if  all 
the  benefits  and  sacrifices  involved  are  doubled  or  halved  or  increased 
or  decreased  in  any  common  ratio.  Let  us  then  divide  them  all  by 
1.19i  Then  we  would  have  $91. 3  paid  in  1870  for  $100  due  in  1879, 
and  $5.02  per  annum  in  the  meantime.  That  is,  the  rate  of  interest 
realized  is  exactly  as  if  the  bond  were  a  5.02  per  cent,  bond  maturing 
in  1879  and  bought  at  91.3  in  1870.  This  rate  can  readily  be  obtained 
from  the  bond  tables  by  interpolating  between  the  figures  for  a  5 
per  cent,  and  a  5^  per  cent,  bond  purchased  at  91.3  with  9  years  to  run. 
For  a  5  per  cent,  bond  we  obtain  6.28  per  cent,  and  for  a  52  per  cent, 
bond,  6.81  per  cent.  Hence  for  a  5.02  per  cent,  bond  the  result  is 
6.30  per  cent. 

The  third  column  gives  what  may  be  called  the  expected  rate  of 
appreciation  of  currency  in  terms  of  gold ;  that  is,  that  rate  of  appre- 
ciation which  would  have  made  the  two  interest  rates  equally  profit- 
able.    It  is  therefore  the  difference  between  the  two  rates  of  interest. 

Finally,  the  last  column  gives  the  actual  rate  of  appreciation  be- 
tween the  dates  mentioned  and  January  1,  1879.  This  is  calculated 
from  the  quoted  prices  of  gold.  Thus  the  opening  price  of  gold 
January,  1870,  was  119.9,  and  January,  1879,  100.  Hence  currency 
appreciated  in  nine  years  in  the  ratio  of  100  to  119.9,  which  is  at  the 
rate  of  2.1  per  cent,  per  annum.  If  the  appreciation  proceeded  uni- 
formly, this  method  would  be  strictly  correct.  As  it  is,  a  more  elabo- 
rate method  would  be  required,  in  accordance  with  the  principles 
explained  in  §  9  of  the  Appendix  to  Chap.  V,  to  take  account 
fully  of  the  fluctuations  of  the  annual  appreciation.  But  for  our 
present  purposes,  and  for  results  worked  out  to  but  one  decimal 
place,  the  simpler  method  here  adopted  is  sufficiently  correct. 


264  THE  RATE  OF  INTEREST  [Chap.  XIV 

From  this  table  we  see  that  the  rates  of  interest  realized 
for  the  period,  January,  1870  to  January,  1879,  were  in 
coin,  7.1  per  cent.,  and  in  currency,  6.3  per  cent.,  the  dif- 
ference ^  between  which  is  .8  per  cent.,  the  rate  of  apprecia- 
tion which  would  equalize  the  investments  in  the  two  bonds- 
This  may  be  called  the  "expected  appreciation."  The 
actual  rate  of  appreciation  was  2.1  per  cent.  That  is, 
the  estimated  appreciation  was  about  two-fifths  of  the  ap- 
preciation as  it  really  turned  out.  Those  who  held  currency 
sixes  therefore  had  the  better  investment  during  1870- 
1879.  In  fact,  it  is  well  known  that  many  speculators 
grew  rich  by  exchanging  gold  bonds  for  currency  bonds 
about  this  time.  The  table  shows  that  there  was  the 
same  underestimate  of  future  appreciation  in  July,  1870, 
January,  1871,  and  July,  1871.  From  that  time  to  July, 
1874,  the  table  shows  that  the  outlook  for  resumption 
grew  gloomy,  due  no  doubt  to  the  strong  greenback  senti- 
ment. The  inflation  bill  of  1874  actually  produced  a 
prospect  of  negative  appreciation;  i.e.  depreciation.  This 
bill  was  vetoed  by  President  Grant,  and  in  December 
of  that  year  the  bill  for  resumption  was  passed  by  the 
Senate.  Accordingly,  January,  1875,  opened  with  a  more 
hopeful  estimate.  The  bill  became  a  law  on  the  14th  of 
January,  and  there  was  an  immediate  rise  in  the  "expected 
appreciation"  which  from  that  time  forward  averaged 
2  per  cent.     But  during  the  same  period  the  actual  ap- 

*  The  formula  used  is  therefore  simply  /  =  i  +  o.  (/  represents  the 
rate  of  interest  in  coin,  i  the  rate  of  interest  in  currency,  a  the  expected 
rate  of  appreciation  —  that  is,  the  rate  of  appreciation  of  the  cur- 
rency standard  with  respect  to  the  coin  standard).  As  shown  in  Ap- 
pendix to  Chap.  V,  §  3,  this  formula  applies  strictly  only  when  the 
rates  of  interest  and  of  appreciation  are  "reckoned  continuously." 
But  practically  it  applies  to  all  cases  with  which  we  have  to  deal, 
as  the  interest  periods  are  seldom  over  half  a  year.  Even  when  the 
interest  is  payable  only  annually,  and,  in  consequence,  the  correct 
formula  is  1  -I-  /  =  (1  +  t)  (1  +  «).  (see  Appendix  to  Chap.  V,  §  2), 
the  value  of  a  calculated  by  this  formula  will  seldom  differ  perceptibly 
from  its  value  calculated  by  the  simpler  formula  j  =  i  +  a,  here 
employed. 


Sec.  4]       INDUCTIVE  VERIFICATION   (MONETARY)  265 

preciation  from  the  dates  named  to  January,  1879,  averaged 
3.6.  per  cent.,  so  that  even  after  the  government  promised 
resumption,  investors  and  speculators  did  not  put  imphcit 
confidence  in  that  promise,  the  "expected  appreciation" 
being  only  a  little  more  than  half  the  actual  appreciation. 
This  corresponds  to  the  well-known  fact  that  the  resump- 
tion act  was  looked  upon  as  a  political  maneuver,  likely 
to  be  repealed.^ 

§  4 

Having  compared  the  rates  of  interest  in  paper  and 
coin,  we  may  next  compare  them  in  gold  and  silver.  The 
comparison,  to  be  of  value,  must  be  between  gold  and  silver 
contracts  in  the  same  market  and  with  the  same  secm'ity. 
Such  contracts  are  fortunately  available  in  the  London 
market   of   government    securities.     The   loans   of   India 

*  It  should  be  observed  that  the  method  employed  to  determine 
the  rate  of  interest  realized  is  open  to  one  danger.  It  correctly  repre- 
sents the  rate  of  interest  actually  realized  between  two  dates,  but, 
unless  the  later  of  the  two  dates  is  maturity,  it  does  not  necessarily 
represent  the  rate  of  interest  expected  at  the  first  date.  The  investor 
could  not  know  in  January,  1870,  what  the  price  of  bonds  would  be 
in  January,  1879,  unless  the  bonds  matured  at  that  time.  To  accu- 
rately compare,  in  1870,  the  relative  advantages  of  coin  and  currency 
bonds  for  the  period  1870-1879,  a  forecast  would  have  been  necessary, 
not  only  of  the  relation  of  currency  to  gold,  but  also  of  the  prices  of 
the  two  bonds  in  1879.  These  prices,  in  turn,  depend  on  a  new  fore- 
cast made  in  1879.  It  follows  that  a  mistake  in  this  forecast  of  1879 
and  embodied  in  the  prices  of  that  year  woiild  affect  the  rate  of  in- 
terest realized  between  1870  and  1879  in  the  same  manner  as  a  mis- 
take of  the  opposite  kind  in  the  forecast  of  1870. 

But  in  most  cases  the  method  given  is  sufficiently  exact.  For, 
although  in  1870  it  would  have  been  impossible  to  predict  exactly 
the  prices  of  the  two  bonds  in  1879,  yet  it  can  usually  be  depended 
upon  that  any  great  change  in  price  is  apt  to  affect  both  alike,  and 
thus  eliminates  itself  for  the  most  part  in  the  comparison.  The  reason 
that  the  errors  in  predicting  what  the  prices  of  the  two  bonds  would 
be  in  1879  are  nearly  equal  is  that  the  two  bonds  selected  were  ap- 
proximately of  the  same  term.  The  coin  bonds  matured  in  1907, 
the  currency  bonds  in  1898  and  1899.  The  eight  or  nine  years  be- 
tween them  would  be  almost  immaterial  in  1879.  It  is  for  this  reason 
that  the  coin  bonds  of  1907  were  chosen  in  preference  to  those  of 
1881. 


266 


THE   RATE  OF   INTEREST 


[Chap.  XIV 


have  been  made  partly  in  gold  and  partly  in  silver,  and 
both  forms  of  securities  are  bought  and  sold  in  London/ 
The  interest  on  the  silver,  or  rather  rupee,  bonds  is  paid 
by  draft  on  India.  The  sums  actually  received  in  English 
money  depend  on  the  state  of  the  exchanges.  The  rate 
of  interest  in  the  silver  standard  is  calculated  in  the  same 
way  as  was  shown  ^  for  coin  bonds  in  §  3.  The  results  are 
contained  in  the  following  table :  — 

RATES  OF  INTEREST  REALIZED  FROM  DATES  NAMED 
TO    MATURITY    OR    IN    PERPETUITY  3 


Rupee 

Gold 

Differ- 
ence 

Exchange  on 

India 

Pence  per  Rupee 

1865 

4.3 

4.1 

.2 

23.2 

1868 

4.3 

4.0 

.3 

23.0 

1870 

4.3 

4.0 

.3 

23.6 

1871 

4.1 

3.8 

.3 

23.2 

1872 

3.9 

3.7 

.2 

22.6 

1873 

3.9 

3.7 

.2 

22.4 

1874 

3.9 

3.8 

.1 

22.2 

*  The  silver  bonds  or  "rupee  paper"  were  issued  to  raise  loans  in 
India,  but  they  have  also  been  enfaced  for  payment  in  England,  and 
in  1893-1894  some  Rs.  25,000,000  were  on  the  London  books.  —  Bur- 
dett's  Official  Intelligencer  (1894),  p.  75. 

^  Thus  in  1880  the  average  price  paid  in  London  for  "rupee  paper" 
efface  value  Rs.  1,000  yielding  4  per  cent.,  or  Rs.  40  per  annum,  was 
£79.  In  order  to  find  the  rate  of  interest  realized  by  the  investor, 
we  must  translate  £79  into  silver.  The  average  rate  of  exchange 
in  1880  was  20d.  per  rupee.  Hence  £79  were  equivalent  to  948 
rupees.  That  is,  speaking  in  terms  of  silver  (or,  more  exactly,  in 
terms  of  exchange  on  India),  the  price  of  a  4  per  cent,  bond  was  94.8, 
which,  if  the  bond  be  treated  as  a  perpetual  annuity,  yields  the  in- 
vestor 4.3  per  cent.  In  the  same  year,  an  India  gold  bond  yielded 
3.6  per  cent. 

^  This  table  is  formed  from  averages  of  (usually  ten)  quotations 
distributed  through  each  year,  taken  from  the  Economist,  the  In- 
vestor's Monthly  Manual,  and  the  (London)  Bankers'  Magazine.  The 
fourth  column  is  founded  on  the  table  in  the  Report  of  the  Indian  Cur- 
rency Committee  (1893),  p.  27,  but  is  corrected  to  apply  to  calendar 
instead  of  official  years. 


Sec.  4]      INDUCTIVE  VERIFICATION   (MONETARY) 


267 


RATES  OF  INTEREST  REALIZED   FROM   DATES   NAMED 
TO  MATURITY  OR   IN  PERPETUITY— Conhnweti 


Rupee  ' 

Gold  2 

Differ- 
ence 

Exchange  on 

India 

Pence  per  Rupee 

1875 

4.0 

3.6 

.4 

21.9 

1876 

4.1 

3.7 

.4 

20.5 

1877  ' 

4.1 

3.7 

.4 

20.9 

1878 

4.2 

3.9 

.3 

20.2 

1879 

4.4 

3.7 

.7 

19.7 

1880 

4.3 

3.6 

.7 

20.0 

1881 

4.0 

3.4 

.6 

19.9 

1882 

3.9 

3.5 

.4 

19.5 

1883 

4.1 

3.4 

.7 

19.5 

1884 

4.1 

3.3 

.8 

19.5 

1885 

4.1 

3.5 

.6 

18.5 

1886 

4.1 

3.5 

.6 

17.5 

1887 

4.1 

3.4 

.7 

17.2 

1888 

4.1 

3.1 

1.0 

16.5 

1889 

4.1 

3.0 

1.1 

16.5 

1890,  1st  half 

4.0 

3.0 

1.0 

17.6 

1890,  2d  half 

3.9 

3.1 

.8 

19.3 

1891 

3.8 

3.1 

.7 

17.1 

1892 

3.9 

3.1 

.8 

15.3 

1893 

3.9 

3.0 

.9 

15.0 

1894 

3.9 

3.0 

.9 

13.5 

*  The  quotation  from  which  the  interest  was  computed  for  1895 
and  succeeding  years  is  for  3^  per  cent,  rupee  paper.  All  previous 
quotations  are  for  4  per  cent.'s.  The  4  per  cent.'s  were  repayable  on 
three  months'  notice;  this  notice  was  given  in  1894,  and  the  bonds 
redeemed  or  converted  into  3^  per  cent.'s  before  the  close  of  the  year. 
To  obtain  the  rate  of  interest  realized,  the  London  quotations  in 
pounds  sterling  are  first  converted  into  rupees  at  the  current  rates  of 
exchange,  and  then  the  bonds  are  treated  as  perpetual  annuities. 
The  results  differ  from  those  given  in  the  Investor's  Monthly  Manual, 
because  the  rupee  is  there  converted  at  a  conventional  value,  not  the 
market  value. 

^  From  1865  to  1880  inclusive  the  figures  refer  to  4  per  cent.'s, 
repayable  October,  1888,  or  later;  those  of  1881-1884  are  for  3^  per 
cent.'s  maturing  in  1931,  and  those  for  1885-1906  are  for  3  per 
cent.'s  maturing  in  1948. 


268 


THE  RATE  OF  INTEREST 


[Chap.  XIV 


RATES  OF  INTEREST  REALIZED  FROM  DATES  NAMED 
TO  MATURITY  OR  IN  PERPETUITY  — Conduced 


Rupee 

Gold 

Differ- 
ence 

Exchange  on 

India 

Pence  per  Rupee 

1895 

3.4 

2.8 

.6 

13.4 

1896 

3.3 

3.1 

.2 

14.3 

1897 

3.5 

3.1 

.4 

15.1 

1898 

3.7 

3.2 

.5 

16.0 

1899 

3.6 

3.2 

.4 

10.1 

1900 

3.7 

3.4 

.3 

16.0 

1901 

3.7 

3.5 

.2 

16.0 

1902 

3.6 

3.5 

.1 

16.0 

1903 

3.5 

3.5 

.0 

16.0 

1904 

3.6 

3.7 

-.1 

16.1 

1905 

3.6 

3.6 

.0 

16.1 

1906 

3.6 

3.2 

.4 

16.0 

From  this  table  it  will  be  seen  that  the  rates  realized 
to  investors  in  bonds  of  the  two  standards  differed  but 
slightly  until  1875,  when  the  fall  of  Indian  exchange  began. 
The  average  difference  previously  to  1875  was  .2  per  cent., 
while  the  average  difference  from  1875  to  1892  inclusive 
was  .7  per  cent.,  or  more  than  three  times  as  much.  Within 
this  period,  from  1884  exchange  fell  much  more  rapidly 
than  before,  and  the  difference  in  the  two  rates  of  interest 
rose  accordingly,  amounting  in  one  year  to  1.1  per  cent. 
Inasmuch  as  the  two  bonds  were  issued  by  the  same  gov- 
ernment, possess  the  same  degree  of  security,  are  quoted 
side  by  side  in  the  same  market,  and  are  similar  in  all  other 
respects  except  in  the  standard  in  which  they  are  expressed, 
the  results  afford  substantial  proof  that  the  fall  of  exchange 
(after  it  once  began)  was  discounted  in  advance  and  af- 
fected the  rates  of  interest  in  those  standards.  Of  course 
investors  did  not  form  perfectly  definite  estimates  of  the 
future  fall,  but  the  fear  of  a  fall  predominated  in  varying 
degrees  over  the  hope  of  a  rise. 


Sec.  4]       INDUCTIVE  VERIFICATION   (MONETARY)  269 

The  year  1890  was  one  of  great  disturbance  in  exchanges, 
the  average  for  the  first  six  months  being  17.6  and  for  the 
last  six  months  19.3.  The  gold  price  of  the  silver  bonds 
rose  from  an  average  for  the  first  six  months  of  73.8  to  83.5 
for  the  last  six  months,  but  the  rise  in  their  silver  price 
was  only  from  100.6  to  103.7,  showing  that  the  increase  of 
confidence  in  the  "future  of  silver"  was  not  great,  and  in 
fact  only  reduced  the  disparity  in  the  interest  from  1.0 
to  .8  per  cent. 

This  great  rise  in  exchange  and  the  slight  revival  in  silver 
securities  occurred  simultaneously  with  the  passage  of 
the  Sherman  Act  of  July,  1890,  by  which  the  United  States 
was  to  purchase  four  and  a  half  million  ounces  of  silver  per 
month.  There  can  be  little  doubt  that  the  disturbance 
was  due  in  some  measure  to  the  operation  or  expected 
operation  of  that  law. 

This  is  not  the  only  case  in  which  the  relative  prices  of 
rupee  paper  and  gold  bonds  were  probably  affected  by 
poUtical  action.  One  of  the  smallest  differences  in  the  two 
rates  occurs  in  1878,  which  was  the  year  of  the  Bland  Act 
and  the  first  international  monetary  conference. 

After  the  closure  of  the  Indian  mints  on  June  26,  1893, 
exchange  rose  from  14.7  to  15.9,  the  gold  price  of  rupee 
paper  from  62  to  70,  and  consequently  its  rupee  price  from 
101.2  to  105.7.  From  this  point  the  exchange  again 
dropped,  much  to  the  mystification  of  those  who  had  pre- 
dicted an  established  parity  between  gold  and  silver  at  the 
new  legal  rate  of  16d.  per  rupee.  There  was  much  dis- 
cussion as  to  the  reasons  for  the  failure  of  the  legal  rate 
to  become  operative.  The  reason  seems  to  have  been  that 
the  closure  of  the  mints  to  silver  attracted  into  the  cir- 
culation silver  from  other  channels,  especially  old  Native 
hoards.  Within  a  few  years,  however,  this  source  of  supply 
was  dried  up  so  that  the  legal  par  was  reached  in  1898  and 
has  been  maintained  ever  since,  subject  only  to  the  slight 
variations  of  exchange  due  to  the  cost  of  shipping  specie. 
But  until  the  par  was  proved  actually  stable  by  two  or 


270  THE  RATE  OF  INTEREST  [Chap.  XIV 

three  years'  experience,  the  public  refused  to  have  confi- 
dence that  gold  and  the  rupee  were  once  more  to  run 
parallel.  Their  lack  of  confidence  was  shown  in  the  dif- 
ference in  the  rates  of  interest  in  gold  and  rupee  securi- 
ties during  the  transition  period,  1893-1898,  and  the  two 
or  three  succeeding  years.  From  1893  to  1900  inclusive 
the  two  rates  averaged  .5  per  cent,  apart.  From  1901  to 
1906  inclusive,  the  average  difference  was  only  .1  per  cent.^ 

§  5 

We  shall  next  attempt  to  apply  the  theory  of  appreciation 
and  interest  to  periods  of  rising  and  falling  prices.  We 
are  met,  however,  by  the  difficulty  that  comparison  can 
only  be  made  between  successive  periods.  We  can  learn 
what  the  rate  of  interest  has  been  during  a  price  movement, 
but  we  cannot  know  what  it  would  have  been  if  that  price 
movement  had  not  taken  place.  Without  this  missing 
term  of  comparison,  it  is  difficult  to  measure  the  influence 
of  the  rise  or  fall  in  price  level.  No  two  periods  are  so  alike 
industrially  that  we  can  say  they  differ  only  in  the  state 
of  the  monetary  standard.  Other  influences  innumerable 
affect  the  "value  of  money."  In  spite  of  these  diflficulties, 
however,  certain  general  conclusions  can  be  established. 

It  must  be  borne  in  mind  that  we  are  studying  the  effects 
of  rising,  not  high,  prices,  and  of  falling,  not  low,  prices. 
Falling  prices  are  as  different  from  low  prices  as  a  waterfall 
is  from  sea  level.  Our  study  is  not  of  price  levels,  but  of  the 
slopes  between  price  levels.^ 

'  The  preceding  comparisons  serve  only  to  establish  the  influence 
of  the  divergence  between  the  standards  on  the  rates  of  interest, 
but  afford  no  measure  of  that  influence.  In  order  to  measure  the 
extent  to  which  the  fall  of  silver  was  allowed  for  by  investors,  it  would 
be  necessary  to  examine  the  rates  realized  during  specific  periods, 
as  in  the  case  of  coin  and  currency  bonds  considered  in  §  3.  A  some- 
what unsatisfactory  attempt  to  do  this  was  made  in  "Appreciation 
and  Interest,"  but  is  not  reproduced  here.  The  case  is  unlike  that 
of  the  United  States  coin  and  currency  bonds,  since  in  the  case  now 
under  discussion,  the  two  kinds  of  bonds,  rupee  and  gold,  did  not 
have  approximately  the  same  date  of  maturity. 

'  De  Haas  appears  to  have  fallen  into  the  confusion  between  high 


Sec.  5  ]     INDUCTIVE  VERIFICATION   (MONETARY)  271 

It  was  once  predicted  by  Mr.  H.  H.  Gibbs/  formerly  a 
director  of  the  Bank  of  England,  that  the  progressive 
scarcity  of  gold  would  raise  the  rate  of  interest.  He 
reasoned  that  such  scarcity  would  make  a  stringency  in 
the  money  market,  and  that  the  banks,  each  struggling  to 
attract  reserves  from  the  others,  would  raise  their  rates. 
This  prophecy,  however,  was  not  fulfilled.  The  theory  that 
appreciation  raises  interest  has  been  frecpently  affirmed, 
and  has  even  received  the  stamp  of  approval  of  Mr.  Robert 
Giffen.     But  it  is  utterly  at  variance  with  facts.^ 

When  prices  are  rising  or  falling,  money  is  depreciating 
or  appreciating  relatively  to  commodities.  Our  theory  would 
therefore  require  high  or  low  interest  according  as  prices 
are  rising  or  falling,  provided  we  assume  that  the  rate  of 
interest  in  the  commodity  standard  does  not  vary.  This 
assumption  would  be  thoroughly  justified  only  in  case  the 
two  periods  were  alike  in  all  respects  except  in  the  expansion 
or  contraction  of  credit  and  currency. 

In  the  following  table  for  London  the  periods  are  selected 
to  correspond  with  the  main  movements  of  prices.  Thus, 
the  period  1826-1829  was  a  period  of  falling  prices,  so  that 
money  appreciated  in  terms  of  commodities  at  the  average 
rate  of  4.2  per  cent,  per  annum.  This  is  indicated  in  the 
third  column  by  the  figure  +  4.2.  In  the  period  1836-1839 
prices  rose  so  that  money  fell  at  the  rate  of  2.3  per  cent,  per 
annum,  indicated  by— 2.3.  The  fourth  and  last  column 
indicates  the  rate  of  interest  which  is  virtually  paid  in  com- 
modities. It  is  the  rate  of  commodity-interest  ecpivalent 
to  the  market  rate  of  money-interest  actually  paid,  and 
therefore  is,  in  each  case,  the  sum  of  the  two  items  of  the 
two  preceding  columns. 

and  rising  prices,  both  in  his  criticism  of  Jevons  and  in  his  treatment 
of  statistics.  See  "A  Third  Element  in  the  Rate  of  Interest,"  Jour- 
nal of  the  Royal  Statistical  Society,  March,  1889. 

1  The  Bimetallic   Controversy,  London  (Wilson),  1886,  pp.  19,  231 
245-249,  373. 

'  See  "Appreciation  and  Interest,"  p.  57. 


272 


THE  RATE   OF  INTEREST 


[Chap.  XIV 


LONDON  RATES  OF  INTEREST  IN  RELATION  TO  RISING 
AND    FALLING    PRICES' 


Virtual 

Appreciation 

Interest  in 

Bank 

Market 

OF  Money  in 

Commodities 

i 

Commodities 
a 

(Market) 

1826-1829 

4.4 

3.5 

+  4.2 

7.7 

1830-1835 

4.0 

3.2 

0.0 

3.2 

1836-1839 

4.7 

4.2 

-2.3 

1.9 

1840-1844 

4.2 

3.5 

+  5.9 

9.4 

,     1845-1847 

3.7 

4.2 

-3.0 

1.2 

1848-18.52 

2.9 

2.5 

+  1.2 

3.7 

1853-1857 

4.1 

5.3 

-2.4 

2.9 

1858-1864 

4.4 

4.2 

-3.0 

1.2 

1865-1870 

3.8 

3.6 

+  1.1 

4.7 

1871-1873 

3.9 

3.7 

-6.2 

-2.5 

1874-1879 

3.2 

2.7 

+  4.3 

7.0 

1880-1887 

3.3 

2.6 

+  3.8 

6.4 

1888-1890 

3.8 

2.9 

-1.4 

1.5 

1891-1896 

2.5 

1.5 

+  3.4 

4.9 

1897-1900 

3.2 

2.6 

-6.6 

-4.0 

1901-1906 

3.6 

3.1 

-1.5 

1.6 

'  This  table  is  constructed  from  the  data  given  in  the  Appendix 
to  this  chapter.  The  third  column  is  based  on  index  numbers  (Jevons' 
for  1826-1852,  and  Sauerbeck's  for  the  remaining  years).  The  index 
numbers  for  two  dates,  as  1826  and  1829,  being  given,  their  inverse 
ratio  gives  the  relative  value  of  money  (in  commodities)  at  those 
two  dates.  From  these  it  is  easy  to  calculate  the  average  annual 
change  in  its  value.  The  method  is  the  same  as  that  employed  for 
finding  the  rate  of  interest  by  which  $1,  by  compounding,  will 
amount  to  a  given  sum  in  a  given  time.  Theoretically,  since  the 
loans  here  included  run  usually  perhaps  thirty  to  ninety  days,  the 
quotations  of  rates  of  interest  averaged  should  begin  at  the  first  of 
the  two  dates,  and  cease,  say,  sixty  days  before  the  second.  But  the 
index  numbers  are  not  always  for  definite  points  of  time,  nor  can 
the  interest  quotations  be  subjected  to  such  minute  corrections  with- 
out an  immense  expenditure  of  labor.  Hence,  the  method  adopted 
has  been  to  average  the  rates  for  all  the  years  of  a  period;  e.g.  for 
the  four  years,  1826-1829.  The  "appreciation"  is  reckoned  between 
those  dates.  If  the  index  numbers  represent  the  price  levels  at  the 
middle  of  1826  and  1829,  then  the  average  interest  rates  ought  in 
theory  to  include  only  the  last  six  months  of  1826,  and  the  first 
four  months  of  1829.  But  it  seems  better  to  include  too  much  at 
both  ends  than  to  omit  the  averages  for  1826  and  1829  altogether, 
for  the  reason  that  an  average  is  the  more  valuable  the  greater  the 
number  of  terms  included. 


Sec.  6]       INDUCTIVE  VERIFICATION   (MONETARY)  273 

If  this  table  be  examined,  it  will  be  found  that  if,  in 
comparing  one  period  with  the  next,  the  rate  of  interest 
falls,  the  "appreciation"  usually  rises,  or  if  the  rate  rises, 
the  "  appreciation  "  falls.  The  comparison  of  each  period 
with  the  one  following  may  be  designated  as  a  "se- 
quence." In  twelve  out  of  fifteen  sequences  for  bank  rates 
and  in  eleven  out  of  fifteen  for  market  rates,  interest 
is  high  or  low  according  to  the  degree  in  which  prices  are 
rising  or  falling.  Attention  is  called  particularly  to  the 
period  1853-1857,  during  which  prices  rose  very  fast  simul- 
taneously with,  and  presumably  because  of,  the  great  gold 
production.  The  market  rate  of  interest  averaged  5.3 
per  cent.,  which  was  far  higher,  not  only  than  in  any  sub- 
sequent, but  also  than  in  any  previous  period. 

§  6 

The  following  table  for  Berlin  displays  the  same  connec- 
tion between  price  movements  and  interest :  — 

BERLIN  RATES  OF  INTEREST  IN  RELATION  TO  RISING 
AND    FALLING    PRICES' 


Apprecia- 

Virtual 

Virtual 

tion  OF 

Interest  in 

Interest  in 

Bank 

Market 

Money  in 

Commodities 

Commodities 

Commodities 

(Bank) 

(Market) 

I 

t 

a 

1 

1 

1851-1852 

4.0 

— 

-1.5 

2.5 

— 

1853-1857 

4.7 

— 

-3.3 

1.4 

— 

1858-1864 

4.3 

3.7* 

-2.2 

2.1 

1.5 

1865-1870 

4.7 

4.0 

0.0 

— 

4.0 

1871-1873 

4.5 

4.1 

-4.1 

— 

0.0 

1874-1879 

4.3 

3.2 

+  3.1 

— 

6.3 

1880-1883 

4.3 

3.4 

-0.1 

— 

3.3 

1884-1888 

3.6 

2.5 

+  2.9 

— 

5.4 

1889-1891 

4.0 

3.1 

-1.4 

— 

1.8 

1892-1895 

3.4 

2.2 

+  5.2 

— 

7.4 

1896-1899 

4.2 

3.6 

-6.8 

— 

-3.2 

1900-1902 

4.2 

3.2 

5.4 

— 

8.6 

1903-1905 

3.9 

3.0 

-  1.4 

— 

1.6 

*  This  table  is  constructed  from  the  data  in  the  Appendix.     The 
average  in  the  second  column  marked  (*)  is  for  the  years  1861-1864, 

T 


274 


THE  RATE  OF  INTEREST 


[Chap.  XIV 


In  the  foregoing  table  the  relation  between  appreciation 
and  interest  is  observed  in  seven  out  of  twelve  sequences 
for  bank  rates  (two  being  neutral)  and  in  eight  out  of  ten, 
for  market  rates. 

For  France,  index  numbers  covering  a  wide  range  of 
articles  are  not  available.  Using  those  given  in  the  "  Aid- 
rich  Report"  for  sixteen  articles,  we  have  :  — 

PARIS  RATES  OF  INTEREST  IN  RELATION  TO   RISING 
AND    FALLING    PRICES' 


Appreciation 

Bank 

Market 

OF  Money  in 
Commodities 

1861-1864 

5.1 

-8.1 

186.5-1870 

3.2 

+  3.6 

1871-1873 

5.3 

4.6* 

-4.5 

1874-1879 

3.1 

2.6 

+  4.3 

1880-1886 

3.2 

2.8 

+  2.3 

1887-1890 

3.1 

2.6 

-5.1 

1891-1895 

2.6 

2.0 

Here  the  same  connection  is  observed  in  five  out  of  six 
sequences  for  bank  rates  and  three  out  of  four  for  market 
rates.^ 

It  will  be  noted  that  the  course  of  prices  and  interest 
has  been  very  much  the  same  in  England,  Germany,  and 
France. 

For  New  York  we  have  the  following  table :  — 


not  1858-1864.  The  "appreciation"  to  1891  is  calculated  from  the 
figures  of  Soetbeer  and  Heinz,  as  given  in  the  "Aldrich  Report" 
of  1893  of  the  U.  S.  Senate  on  Wholesale  Prices.  The  figures  for  the 
later  years  are  taken  from  The  London  Economist  and  from  A.  Soet- 
beer's  tables  in  the  Journal  of  the  Royal  Statistical  Society,  Vol. 
LXVII,  Part  I,  pp.  85,  89. 

'■  This  table  is  constructed  from  the  data  in  the  Appendix.  The 
average  in  the  second  column  marked  (*)  is  for  the  years  1872-1873, 
not  1871-1873. 

^  Assuming  that  prices  fell,  1891-1895. 


Sec.  6]       INDUCTIVE  VERIFICATION   (MONETARY) 


275 


NEW    YORK   RATES   OF   INTEREST    IN   RELATION   TO 
RISING  AND  FALLING  PRICES  i 


Prime 

Apprecia- 
tion OF 

Virtual 
Interest  in 
Commodities 

(60  Days) 

Virtual 
Interest  in 

Call 

60 
Days 

Two 

Name 

60  Days 

Money  in 

Commod- 
ities 

Commod- 
ities 
(Prime) 

i 

I 

a 

1 

? 

1849-1857 

6.2 

9.2 

— 

-3.8 

5.4 



1858-1860 

5.0 

7.4 

— 

+  6.4 

13.8 

1861-1865 

5.9 

8.4 

6.8 

-20.2 

-11.8 

-13.4 

1866-1874 

5.4 

8.4 

7.5 

+  4.7 

13.1 

12.2 

1875-1879 

— 

— 

5.1 

+  7.9 

13.0 

1880-1884 

— 

— 

5.4 

+  0.6 



6.0 

1885-1891 

— 

— 

5.1 

-0.2 

4.9 

1892-1897 

— 

— 

4.6 

+  5.6 

10.2 

1898-1906 

— 

— 

4.6 

-3.5 

1.1 

We  find  here  the  same  association  of  appreciation  and 
interest  in  all  of  the  three  sequences  for  call  loans,  in  two 
of  the  three  cases  for  60-day  paper  (the  third  being  neutral) , 
and  in  three  of  the  six  cases  for  "prime"  paper  (one  being 
neutral). 

Perhaps  the  most  remarkable  feature  of  this  table  is  the 
extremely  low  rate  for  1875- 1879.  The  extraordinary  change 
in  interest  rates  beginning  in  1875  has  been  observed  before ; 
but  its  connection  with  the  resumption  act  (as  it  seems  to  the 
writer)  has  been  misconstrued.^ 

*  This  table  is  constructed  from  the  data  in  the  Appendix.  The 
rates  of  appreciation  are  calculated  from  Falkner's  figures  for  prices 
and  wages  in  the  "Aldrich  Report." 

^  Thus  William  Bro ugh,  referring  to  that  act,  says:  "The  mere 
announcement  of  our  intention  to  put  our  money  on  a  sound  metal- 
lic basis  had  brought  capital  to  us  in  such  abundance  that  the  resump- 
tion was  not  only  made  easy,  but  the  normal  rate  of  interest  was 
reduced.  .  .  .  This  remarkable  reduction  ...  is  explainable  only 
on  the  ground  of  a  large  reflux  of  foreign  capital."  {Natural  Law 
of  Money,  New  York,  1894,  p.  124.)  If  this  explanation  were  correct, 
we  would  expect  a  still  lower  rate  of  interest  after  resumption  had 
been  accomplished;    but  the  facts  are  the  opposite. 


276 


THE   RATE   OF   INTEREST 


[Chap.  XIV 


§   7 

The  preceding  statistics  apply  to  gold  standard  countries. 
The  following  table  gives  the  rates  of  interest  and  appre- 
ciation for  silver  standard  countries — India,  Japan,  and 
China :  — 


RATES  OF  INTEREST  IN  RELATION  TO  RISING  AND 
FALLING  PRICES  IN  CALCUTTA,  TOKYO,  AND 
SHANGHAI  1 


Bank 

Market 

Appreciation  im 
Commodities 

Calcutta,  1873-1875 

5.3 

+  2.6 

1876-1878 

6.8 

-11.0 

1879-1885 

5.9 

+  3.8 

1886-1889 

6.0 

-2.6 

1890-1893 

4.3 

-4.7 

Tokyo,       1873-1877 

14.0 

12.0 

-0.2 

1878-1881 

16.3 

12.2 

-13.3 

1882-1886 

12.8 

10.3 

+  10.4 

1887-1893 

9.3 

9.4 

-2.8 

1894-1899 

9.7 

11.2 

-5.8 

1900-1902 

11.0 

12.4 

0.0 

Shanghai,  1874-1881 

9.1 

-1.4 

1882-1888 

7.5 

5.8* 

+  1.3 

1889-1893 

7.0 

5.8 

-0.9 

Here  we  find  the  theory  confirmed  in  three  out  of  four 
cases  for  India,  three  out  of  five  for  bank  rates  in  Japan, 
and  three  out  of  five  for  market  rates;  one  out  of  two  for 
bank  rates  in  China,  while  the  one  case  for  market  rates 
is  neutral.^ 

'  This  table  is  constructed  from  the  data  given  in  the  Appendix. 
The  entry  marked  (*)  is  for  1885-1888,  not  1882-1888. 

*  See  also  "  Price  Movements  and  Interest  in  India,"  by  the 
■writer,  in  Yale  Review,  May,  1897,  p.  80. 


Sec.  8]      INDUCTIVE  VERIFICATION   (MONETARY)  277 

Summarizing  the  cases  for  the  seven  countries  examined 
we  find  64  favorable  and  22  unfavorable  to  the  theory,  dis- 
tributed as  follows :  — 


Eng- 
land 

Ger- 
many 

France 

United 

States 

India 

Japan 

China 

Total 

Favorable 
Unfavorable 

23 

7 

15 
5 

8 
2 

8 
2 

3 
1 

6 
4 

1 
1 

64 
22 

The  favorable  cases  are  about  three  times  as  numerous 
as  the  unfavorable  cases.  This  is  a  large  preponderance, 
especially  when  we  consider  that  there  are  so  many  causes 
affecting  the  rate  of  interest  besides  the  mere  appreciation 
or  depreciation  of  the  monetary  standard.  We  therefore 
conclude  with  great  confidence  that,  "other  things  being 
equal,"  the  rate  of  interest  is  relatively  high  when  prices  are 
rising  and  relatively  low  when  prices  are  falling. 

§  8 

The  question  now  arises  whether,  on  the  average,  the 
rate  of  interest  fully  adjusts  itself  to  price-movements. 
This  question  cannot  be  answered  with  perfect  certainty  in 
any  individual  case,  for  the  reason  that  we  have  no  means 
of  knowing  what  the  rate  in  commodities  would  have  been 
had  it  been  possible  to  have  contracts  drawn  in  "  com- 
modities" or  in  a  monetary  standard  which  was  stationary 
with  respect  to  commodities.  We  have,  however,  computed 
the  "virtual"  interest  in  commodities  by  adding  to  the  rate 
of  interest  in  money  the  rate  of  appreciation  of  money  in 
commodities.  Thus  in  London  for  1826-1829  the  rate  of 
interest  in  money  was  3.5  per  cent.,  but  money  was  appre- 
ciating relatively  to  commodities  4.2  per  cent.,  so  that  the 
"virtual  interest,"  or  interest  actually  paid,  translated  in 
terms  of  commodities  (the  forty  commodities  averaged 
by  Jevons) ,  was  7.7  per  cent.  It  will  be  seen  from  the  tables 
that  the  virtual  rate  of  interest  reckoned  in  commodities 


278  THE  RATE  OF  INTEREST  [Chap.  XIV 

usually  varies  inversely  with  the  rate  reckoned  in  money. 
For  1853-1857,  money  interest  was  5.3  per  cent.,  and  for 
1874-1879,  2.7  per  cent. ;  but  commodity-interest  for  1853- 
1857  was  2.9  per  cent,  and  for  1874-1879,  7  per  cent.  There 
are  two  possible  explanations  for  this  inverse  relation.  One 
is  that  when  prices  are  rising  the  cause  may  not  be  monetary 
but  may  lie  in  a  progressive  scarcity  of  commodities  pro- 
duced and  exchanged ;  and,  reversely,  when  prices  are  falling, 
the  cause  may  lie  in  progressive  abundance.  From  the 
theory  of  interest  maintained  throughout  this  book  it 
follows  that  a  progressive  scarcity  of  commodities,  implying 
as  it  does  a  progressive  descending  income  curve,  tends  to 
make  the  rate  of  interest  low;  and  reversely,  progressive 
abundance,  implying  an  ascending  income  curve,  tends  to 
make  interest  high.  When,  therefore,  general  price-move- 
ments represent  changes  in  the  income-stream  of  enjoyable 
services, the  rate  of  ''commodity  interest"  would  naturally 
be  high  when  prices  were  falling  and  low  when  prices  were 
rising,  whatever  might  be  true  of  "  money-interest." 

The  second  possible  reason  that  commodity-interest  and 
money-interest  vary  inversely  during  price-movements  is 
that  these  movements  are  often  imperfectly  foreseen.  The 
high  or  low  rate  in  commodities  is  then  an  abnormal 
phenomenon.  It  is,  as  it  were,  a  trick  played  by  money 
on  those  who  put  too  much  faith  in  its  stability.  Thus, 
during  1898-1905  the  increase  of  prices  in  the  United 
States  is  known  to  have  been  due  largely  to  the  in- 
crease of  gold  production.  There  is  no  evidence  that 
commodities  were  getting  scarce  and  incomes  decreasing, 
but  rather  the  reverse.  There  seems,  therefore,  no  reason 
which  would  justify  the  low  commodity-rate  of  interest 
of  1.8  per  cent,  which  we  found  to  have  been  virtually  paid 
during  that  period.  This  low  rate  must,  in  all  probability, 
have  been  due  to  inadvertence.  The  inrushing  streams  of 
gold  caught  merchants  napping.  They  should  have  stemmed 
the  tide  by  putting  up  interest,  not  only  to  4.6  per  cent.,  as 
they  did,  but  two  or  three  per  cent,  higher. 


Sec.  8]      INDUCTIVE  VERIFICATION   (MONETARY)  279 

Doubtless  both  of  the  causes  play  a  part  in  the  explanation 
of  particular  cases.  Sometimes  commodity-interest  is  low 
during  rising  prices  because  it  is  foreseen  that  the  real  in- 
come-stream is  then  drying  up,  sometimes  because  it  is  not 
foreseen  that  monetary  inflation  is  taking  place,  and  some- 
times for  both  reasons ;  and  reversely,  commodity-interest  is 
high  during  falling  prices,  sometimes  because  of  a  foreseen 
increase  of  the  income-stream,  sometimes  because  of  unfore- 
seen contraction  of  the  currency,  and  sometimes  both. 

It  is  impossible  to  decide  what  part  these  two  factors  — 
foreseen  changes  in  real  income  and  unforeseen  changes  in 
their  monetary  measure  — may  play  in  each  individual  case. 
We  are  too  ignorant  of  the  actual  conditions  behind  the 
scenes.  Nevertheless  there  is  internal  evidence  to  show 
that  in  general  the  latter  factor  —  unforeseen  monetary 
change  —  is  the  more  important.  This  evidence  consists 
in  the  fact  that  commodity-interest  fluctuates  so  widely, 
in  some  cases  even  becoming  negative.  The  following  table 
shows  that  the  mean  variability  or  ''standard  deviation" 
from  the  mean,  which  is  the  best  measure  of  the  fluctuations 
of  any  variable,  is  far  greater  for  the  calculated  or  "virtual" 
rate  of  interest  than  for  the  actual  money  rate  of  interest :  — 


No.  Periods 

Variability 
(Standard  Deviation) 

Market 

Interest 

Virtual 
Interest 

London  .... 
Berlin     .... 
New  York    . 

16 
11 

7 

.88 

.56 

1.06 

3.42 
2.93 
8.43 

The  virtual  interest  in  commodities  is  from  four  to  eight 
times  as  variable  as  the  market  interest  in  money. 

All  these  facts  suggest  —  indeed,  practically  demon- 
strate—  that  money-interest  was  not  adequately  adjusted 
to  the  changes  in  purchasing  power  of  money.  It  is,  of 
course,  not  to  be  assumed  that  commodity-interest  ought 


280  THE  RATE   OF  INTEREST  [Chap.  XIV 

to  be  absolutely  invariable ;  but  it  is  practically  certain  that 
its  variations  could  not  be  three  and  a  half  times  the 
variations  in  money-interest,  unless  the  price-movements 
were  inadequately  predicted.  If  any  doubts  were  possible 
on  this  point  they  must  disappear  when  we  find  that  for 
1871-1873  commodity-interest  in  London  was  minus  2.5 
per  cent.  This  shows  that  money  lenders  would  have  been 
better  off  had  they  simply  bought  commodities  in  1871  and 
held  them  until  1873.  As  it  was,  they  actually  lost  some- 
thing, measured  in  commodities,  as  a  consequence  of 
lending  money.  Such  losses  are  especially  apt  to  appear 
in  short  periods.  Thus  if  we  take  the  period  1824r-1825, 
we  find  that  the  market  rate  was  3.7  per  cent.,  the  rate  of 
appreciation  was  minus  14.5  per  cent.,  and  the  virtual  rate 
of  interest  in  commodities,  minus  10.8  per  cent. ! 

In  New  York  during  the  inflation  period,  1861-1865, 
commodity-interest  sank  to  the  ridiculously  low  figure  of 
minus  13.4  per  cent.  This  shows  in  a  striking  way  how 
thoroughly  the  greenback  inflation  upset  all  business  cal- 
culations, and  how  little  the  investing  public  realized  in 
advance  the  serious  rise  in  prices  of  those  fateful  years. 
That  foresight  was  actually  misguided  at  this  time  is  amply 
confirmed  if  we  examine  the  predictions  as  to  the  termi- 
nation of  the  war  and  the  reduction  of  the  gold  premium, 
which  were  recorded  from  month  to  month  in  the  "  Notes 
on  the  Money  Market"  in  the  (New  York)  Bankers'  Maga- 
zine. In  all  probability  such  errors  of  prediction  are 
common  in  periods  of  paper  money  inflation.  Our  tables 
in  §  7  show  it  for  the  Japanese  inflation  of  1878-1881. 

§  9 

We  can  now  understand  why  a  high  rate  of  interest  need 
not  retard  trade  nor  a  low  rate  stimulate  it.  Tliese  facts 
have  puzzled  many  writers.  For  instance,  Robert  Baxter 
wrote :  ^  — 

'  Journal  of  the  Royal  Statistical  Society,  June,  1876. 


Sec.  9]      INDUCTIVE  VERIFICATION  (MONETARY)  281 

"  Public  inquiry  has  been  of  late  strongly  directed  to  the  reasons 
for  the  very  low  rate  of  interest  upon  loanable  capital  in  the  year 
1875,  the  more  especially  as  ten  years  ago  the  very  high  rates  then 
prevailing  created  equal  surprise." 

And  Jevons  wrote :  ^  — 

"The  effect  of  such  and  many  more  changes  effected  during 
the  last  twenty  years  or  so  is  seen  in  a  general  increase  in  wealth 
and  of  mercantile  industry  and  profits.  Thus  only  can  be  explained 
the  extraordinary  high  rate  at  which  the  interest  of  money  has 
in  the  last  ten  years  often  stood.  During  1854-1857  the  rate  of 
interest  was  only  for  a  few  months  below  5  per  cent.,  but  for  many 
months  above  it.  For  more  than  half  a  year  it  stood  at  6  and  7 
per  cent.,  and  in  the  end  of  1857  it  remained  for  nearly  two  months 
at  10  per  cent.  Again,  in  1861,  interest  rose  to  6  and  8  per  cent., 
and  all  this,  to  the  surprise  of  the  elder  generation,  without  the  general 
stoppage  of  trade,  the  breach  of  credit,  and  the  flood  of  bankruptcy, 
which  has  hitherto  attended  such  rates  of  interest.  It  is  certainly  not  to 
increasing  scarcity  of  capital  we  should  attribute  such  rates,  but 
rather  to  a  greatly  extended  field  for  its  profitable  employment." 

But  were  these  rates  high  ?  If  we  turn  to  our  table  for 
London  rates,  we  find  that  the  average  market  rate  for 
1853-1857  does  appear  to  be  the  highest  in  the  table ;  but, 
unmasking  it  of  the  money  element,  we  find  it  is  equiva- 
lent to  a  commodity-interest  of  2.9  per  cent.  This  is  a  very 
low  rate.  Merchants  with  increasing  prices  and  money 
profits  would  find  it  easy  to  repay  loans  on  such  a  basis. 

Professor  Bonamy  Price, ^  writing  at  a  time  of  very  low 
interest  rates,  says:  — 

"  Every  one  remembers  the  agitations  associated  with  7  per  cent., 
the  trepidation  of  merchants,  the  apprehension  of  losses  in  busi- 
ness. ...  If  only  a  moderate  rate  could  be  reckoned  on  as  steady, 
how  happy  would  every  one  have  been !  .  .  .  Yet  what  are  the 
facts  and  feelings  to-day?  Is  every  merchant,  every  manufac- 
turer rejoicing  in  the  pleasant  terms  on  which  he  obtains  the  ac- 
commodation so  necessary  for  his  business  ?  .  .  .  Alas  I  no  such 
sounds  meet  our  ears.  .  .  .  Commercial  depression  is  the  uni- 
versal cry,  depression  probably  unprecedented  in  duration  in  the 
annals  of  trade,  except  under  the  disturbing  action  of  a  prolonged 

*  Investigations  in  Currency,  p.  95.  (The  italics  are  the  present 
writer's.) 

*  "One  percent,"  Contemporary  Review,  April,  1877.  (The  italics 
are  the  present  writer's.) 


282 


THE  RATE  OF  INTEREST 


[Chap.  XIV 


war.  ...  In  the  export  figures,  the  writer  still  fails  to  see  any 
signs  of  the  long-looked-for  revival  of  trade.  Both  quantities 
and  values  continue  to  shrink  in  all  save  a  few  cases.  .  .  .  What, 
then,  is  the  cause  ?  The  explanation  will  certainly  not  he  found  in 
gold  nor  in  any  form  of  currency  whatever  .  .  .  nor  has  any  one  said 
anything  so  ridiculous.  .  .  .  That  cause  is  one  and  only  one : 
overspending." 

If  we  turn  back  to  the  London  table  we  find,  however, 
that  forl874r-1879the  commodity-rate  of  interest,  so  far  from 
being  low,  was  7  per  cent. !  It  would  be  astonishing  if  trade 
did  not  shrink  under  such  a  burden. 

All  these  writers  mistook  high  or  low  nominal  interest  for 
high  or  low  real  interest.  Tooke  apparently  did  the  same. 
In  his  History  of  Prices,  Vol.  II,  p.  349,  he  names  as  the 
last  of  six  reasons  for  the  fall  of  prices  for  1814-1837,  "a 
reduction  in  the  general  rate  of  interest."  Tliis  is  probably 
not  only  an  inversion  of  cause  and  effect,  but  also,  when  the 
veil  of  money  is  thrown  off,  a  misstatement  of  fact.  The 
commodity-interest  for  1826-1829  was  7.7  per  cent.  Tooke, 
Price,  and  Jevons  all  overlooked  the  fact  that  interest, 
unlike  prices,  is  not  an  instantaneous  but  essentially  a  time 
phenomenon. 

§  10 

Wlien  long  periods  of  price-movements  are  taken,  the 
influence  of  appreciation  on  interest  is  more  certain.  The 
following  table  shows  this  for  England.  It  consists  of 
four  periods,  of  10,  12,  22,  and  11  years  respectively:  — 

LONDON  MARKET  RATES  OF  INTEREST  IN  RELATION 
TO    RISING    AND    FALLING    PRICES 


Market 
Interest 

Appreciation 
OF  Money  in 
Commodities 

Virtual 
Interest  in 
Commodities 

I 

a 

7 

1826-1835 

3.4 

+  1.2 

4.6 

1853-1864 

4.6 

-0.9 

3.7 

1874-1895 

2.4 

+  2.4 

4.8 

1896-1906 

2.9 

-2.9 

0.0 

Sec.  10]      INDUCTIVE  VERIFICATION   (MONETARY)         283 


In  averages  covering  so  many  years  we  may  be  sure  that 
accidental  causes  are  almost  wholly  eliminated.  We  find 
that  during  the  period  of  falling  prices,  1826-1835,  the  aver- 
age rate  of  interest  was  only  3.4;  that  during  the  following 
period  of  rising  prices,  1853-1864,  it  was  higher  (4.6  per  cent.) ; 
that  during  the  next  period,  1874-1895,  when  prices  were 
again  falling,  the  rate  was  again  low  (2.4  per  cent.) ;  and 
finally  that  in  1896-1906,  with  prices  rising,  interest  again 
recovered.  In  every  case  interest  is  high  when  prices  are 
rising  and  low  when  they  are  falling.  For  these  long  periods, 
therefore,  we  find  the  facts  in  agreement  with  the  theory 
in  every  case.  It  is  also  a  noteworthy  fact  that  the  com- 
modity-interest in  this  table  of  long  periods  is  far  less 
variable  than  for  short  periods.  The  variability,  as  shown 
by  the  "  standard  deviation"  of  the  four  figures  in  the  above 
table  is,  for  London,  .82  for  the  market  rate,  and  1.94  for 
the  virtual  rate.  The  adjustment  of  {money)  interest  to  long 
'price-movements  is  more  perfect  than  to  short  price-movements. 

The  following  table  gives  the  long  time  averages  for  New 
York.     Tlie  war  period  is  omitted :  — 

NEW   YORK    RATES    OF   INTEREST    IN    RELATION    TO 
RISING  AND  FALLING  PRICES 


1849-1857 
1875-1896 
1897-1906 


Interest  Prime 

Two  Name 

60  Days 

i 


8.2' 

5.1 

4.5 


Appreciation  of 

Money  in 

Commodities 

a' 


-3.8 
+  2.6 
-3.4 


Virtual  Interest 
IN  Commodities 


4.4 
7.7 
1.1 


We  find  that  the  money  rate  in  the  second  period, 
when  money  was  appreciating,  was,  as  our  theory  requires, 

1  The  average  of  Elliott's  figures  (which  are  not  for  "prime"  paper) 
is  9.2,  but  1.0  has  been  deducted  from  this  average  in  order  that  it  may 
be  properly  compared  with  the  average  of  Robbins's  figures  for  1875- 
1891.  This  correction  is  based  on  the  fact  that  1.0  was  the  average 
excess  of  Elliott's  figures  over  Robbins's  during  the  fifteen  years, 
1860-1874.     See  Appendix  to  Chap.  XIV,  §  1. 


284  THE  RATE   OF   INTEREST  [Chap.  XIV 

lower  than  that  in  the  first,  when  money  was  depreciating, 
but  that  the  rate  in  the  third  period,  when  money  was 
again  depreciating,  was,  unfavorably  to  our  theory,  lower 
than  that  in  the  second  when  money  was  appreciating. 
Here  we  also  see  that  the  variability  of  the  virtual  interest 
in  terms  of  commodities  is  less  than  for  short  periods,  and 
more  nearly  like  the  variability  for  the  market  rate  of 
interest  in  terms  of  money.  The  variability,  as  measured 
by  the  "  standard  deviation,"  of  the  rates  of  interest  for 
the  three  periods  in  the  above  table  are  for  market  rate 
of  interest  in  terms  of  money,  1.6;  for  virtual  interest  in 
terms  of  commodities,  2.3. 

§  11 

Three  general  facts  have  now  been  established :  (1)  Ris- 
ing and  falling  prices  and  wages  are  directly  correlated  with 
high  and  low  rates  of  interest ;  (2)  The  adjustment  of  interest 
to  price-movements  is  inadequate;  (3)  This  adjustment 
is  more  nearly  adequate  for  long  than  for  short  periods. 

These  facts  are  capable  of  a  common  explanation  ex- 
pressing the  manner  in  which  the  adjustment  referred  to 
takes  place.  Suppose  an  upward  movement  of  prices  be- 
gins. Business  profits  (measured  in  money)  will  rise;  for 
profits  are  the  difference  between  gross  income  and  expense, 
and  if  both  these  rise,  their  difference  will  also  rise.  Bor- 
rowers can  now  afford  to  pay  higher  "money-interest." 
If,  however,  only  a  few  persons  at  first  see  this,  the  interest 
will  not  be  fully  adjusted,^  and  borrowers  will  realize   an 

»  It  seems  scarcely  necessary  to  add  as  an  independent  cause  of-, 
maladjustment  the  accumulation  (or  in  the  opposite  case,  depletion) 
of  bank  reserves,  for  this  is  but  another  symptom  of  maladjustment 
due  to  imperfect  foresight.  An  increase  of  gold  supply,  as  in  1852- 
1853  (see  Tooke  and  Newmarch,  History  of  Prices,  Vol.  V,  p.  345), 
may  first  find  its  way  into  the  loan  market  instead  of  into  circulation. 
But  if  foresight  were  perfect,  this  would  not  happen,  or  if  it  did  hap- 
pen, borrowers  would  immediately  take  it  out  (or  increase  the  liabili- 
ties against  it)  to  avail  themselves  of  the  double  advantage  of  low 
interest  and  high  prospective  profits  from  the  rise  of  prices  about  to 
follow. 


Sec.  12]      INDUCTIVE  VERIFICATION   (MONETARY)         285 

extra  margin  of  profit  after  deducting  interest  charges. 
This  raises  an  expectation  of  a  similar  profit  in  the  future 
and  this  expectation,  acting  on  the  demand  for  loans,  will 
raise  the  rate  of  interest.  If  the  rise  is  still  inadequate,  the 
process  is  repeated,  and  thus  by  continual  trial  and  error 
the  rate  approaches  the  true  adjustment. 

\\Tien  a  fall  of  prices  begins,  the  reverse  effects  appear. 
Money  profits  fall.  Borrowers  cannot  afford  to  pay  the 
old  rates  of  interest.  If,  through  miscalculation,  they  still 
attempt  to  do  this,  it  will  cut  into  their  real  profits.  Dis- 
couraged thus  for  the  future,  they  will  then  bid  lower  rates. 

Since  at  the  beginning  of  an  upward  price-movement  the 
rate  of  interest  is  too  low,  and  at  the  beginning  of  a  down- 
ward movement  it  is  too  high,  we  can  understand  not  only 
that  the  averages  for  the  whole  periods  are  imperfectly 
adjusted,  but  that  the  delay  in  the  adjustment  leaves  a 
relatively  low  interest  at  the  beginning  of  an  ascent  of 
prices,  and  a  relatively  high  interest  at  the  beginning  of  a 
descent.  And  this  is  what  we  find  to  be  true.  That  the 
adjustment  is  more  perfect  for  long  periods  than  for  short 
seems  to  be  because,  in  short  periods,  the  years  of  non-ad- 
justment at  the  beginning  occupy  a  larger  relative  part  of 
the  whole  period. 

§  12 

What  has  been  said  bears  directly  on  the  theory  of  "  credit 
cycles."  In  the  view  here  presented,  periods  of  speculation 
and  depression  are  the  result  of  inequality  of  foresight. 
If  all  persons  underestimated  a  rise  of  price  in  the  same 
degree,  the  non-adjustment  of  interest  would  merely  pro- 
duce a  transfer  of  wealth  from  lender  to  borrower.  It  would 
not  influence  the  volume  of  loans  (except  so  far  as  the  diver- 
sion of  income  from  one  person  to  another  would  itself 
have  indirect  effects,  such  as  bankruptcy).  Under  such 
circumstances  the  rate  of  interest  would  be  below  the  nor- 
mal, but   as   no   one  would  know  it,  no  borrower  would 


286  THE  RATE  OF  INTEREST  [Chap.  XIV 

borrow  more  and  no  lender  lend  less  because  of  it.  In  the 
actual  world  however,  foresight  is  very  unequally  distrib- 
uted. Only  a  few  persons  have  the  faculty  of  always 
"coming  out  where  they  look."  Now  it  is  precisely  these 
persons  who  largely  make  up  the  borrowing  class.  Just 
because  of  their  superior  foresight,  there  is  delegated  to 
them  the  management  of  capital ;  they  become  "  captains 
of  industry."  It  therefore  happens  that  when  prices  are 
rising,  borrowers  are  more  apt  to  see  it  than  lenders. 
Hence,  while  the  borrower  is  willing  to  pay  a  higher 
interest  than  before  for  the  same  loan,  lenders  are  willing 
to  loan  for  the  same  interest  as  before.  This  disparity  has 
as  its  effect  that  the  rate  of  interest  will  not  rise  as  high 
as  if  both  sides  saw  the  conditions  equally  well.  It  will 
also  cause  an  increase  of  loans  and  investments.^  This  con- 
stitutes part  of  the  stimulus  to  business  which  takes  place 
in  times  of  rising  prices. 

When  prices  fall,  on  the  other  hand,  borrowers  see  that 
they  cannot  employ  "money"  productively  except  on 
easier  terms,  but  lenders  do  not  see  why  the  terms  should 
be  made  easier.  In  consequence,  "enterprisers"  borrow 
less,  trade  languishes,  and,  though  interest  falls  in  conse- 
quence of  decrease  in  demand,  it  does  not  fall  enough  to 
keep  the  demand  from  decreasing.^ 

We  see,  therefore,  that  while  imperfection  of  foresight 
transfers  wealth  from  creditor  to  debtor  or  the  reverse, 
inequality  of  foresight  produces  overinvestment  during 
rising  prices  and  relative  stagnation  during  falling  prices. 


•  That  this  and  the  corresponding  statement  in  the  next  paragraph 
are  borne  out  by  facts  appears  to  be  confirmed,  so  far  as  bank  loans 
and  discounts  are  concerned,  by  Sumner,  History  of  Banking  in  the 
United  States  (New  York,  1896),  and  Juglar,  Crises  Commerciales 
(Paris,  1889). 

2  President  Andrews,  in  An  Honest  Dollar,  p.  3,  writes:  "Interest 
is  low  .  .  .  not  because  money  is  abundant  as  before,  but  because 
it  is  not,  its  scarcity  having  induced  fall  of  prices,  and  so  paralysis 
in  industry."  But,  it  should  be  added,  the  cause  of  the  fall  of  interest 
is  primarily  the  expectation  of  small  profits. 


Sec.  13]      INDUCTIVE  VERIFICATION   (MONETARY)         287 

In  the  former  case  society  is  trapped  into  devoting  too 
much  investment  of  productive  energies  for  future  return, 
while  in  the  contrary  case,  underinvestment  is  the  rule. 
It  does  not  seem  possible  to  decide  the  question  which  of 
the  two  evils  is  the  greater/ 

§  13 

The  facts  which  have  been  shown  in  this  chapter  are  im- 
portant in  two  respects.  They  prove,  first,  that  men  do 
actually,  even  if  unaware  of  so  doing,  contrive  to  offset  the 
effects  of  changes  in  the  monetary  standard  by  adjusting 
the  rate  of  interest ;  and,  secondly,  that  this  adjustment  is 
far  from  adequate.  In  consequence  of  the  inadequacy 
of  the  interest-adjustment,  a  large  amount  of  wealth  is 
continually  and  unintentionally  transferred  from  the  cred- 
itor- to  the  debtor-class,  and  vice  versa.  The  bimetal- 
lists  were  partially  right  in  their  claim  that  the  creditor- 
class  were  gainers  during  the  period  of  falling  prices  in 
the  two  decades  1875-1895.  The  situation  has  been  the 
exact  opposite  during  the  decade  1896-1906.  We  must 
not  make  the  mistake,  however,  of  assuming  that  the  en- 
richment of  the  debtor-class  during  the  last  decade  atones 
for  the  impoverishment  of  that  class  during  the  previous 
two  decades;    for  the  personnel  of  social  classes  changes 

'  For  arguments  on  both  sides,  see  Professor  Marshall's  evidence, 
Report  on  Depression  of  Trade  (1886),  p.  422.  See  also  his  Principles 
of  Economics,  Vol.  I  (3d  ed.,  1895),  p.  674:  "When  we  come  to  dis- 
cuss the  causes  of  alternating  periods  of  inflation  and  depression 
of  commercial  activity,  we  shall  find  that  they  are  intimately  con- 
nected with  those  variations  in  the  real  rate  of  interest  which  are  caused 
by  changes  in  the  purchasing  power  of  money.  For  when  prices  are 
likely  to  rise,  people  rush  to  borrow  money  and  buy  goods,  and  thus 
help  prices  to  rise;  business  is  inflated,  and  is  managed  recklessly  and 
wastefuUy;  those  working  on  borrowed  capital  pay  back  less  real 
value  than  they  borrowed,  and  enrich  themselves  at  the  expense 
of  the  community.  When  afterwards  credit  is  shaken  and  prices 
begin  to  fall,  every  one  wants  to  get  rid  of  commodities  and  get  hold 
of  money  which  is  rapidly  rising  in  value;  this  makes  prices  fall  all 
the  faster,  and  the  further  fall  makes  credit  shrink  even  more,  and 
thus  for  a  long  time  prices  fall  because  prices  have  fallen." 


288  THE  RATE  OF  INTEREST  [Chap.  XIV 

rapidly.  Nor  must  we  make  the  mistake  of  assuming  that 
the  debtor-class  consists  of  the  poor.  The  typical  debtor 
to-day  is  the  stockholder,  and  the  typical  creditor,  the 
bondholder.  What  is  actually  going  on  to-day  in  conse- 
quence of  a  steadily  cheapening  dollar  is  a  vast  transfer 
of  advantage  from  bondholders  to  stockliolders.  It  is  this 
transfer  which  has  produced  many  of  our  latest  million- 
aires. Tlieir  millions  have  been  silently  abstracted  from 
the  pockets  of  the  unsuspecting  "safe"  investors  in  bonds, 
depositors  in  savings  banks,  and  the  salaried  classes.  The 
fault,  however,  is  not  of  those  who  thus  profit,  but  of  the 
monetary  conditions  which  permit  the  ceaseless  ebb  and 
flow  of  price-levels.  The  problem  of  a  stable  monetary 
standard  is  of  vital  importance.  We  are  apt  to  forget  its 
importance  during  a  period  of  "prosperity,"  and  we  are 
apt  also  to  forget  that  much  of  what  is  called  prosperity 
is  delusive.  It  is  delusive  for  two  reasons:  First,  it  is 
often  not  general  prosperity,  but  prosperity  of  the  debtor 
or  stockholding  or  entrepreneur  classes,  who  are  always 
much  in  evidence,  at  the  expense  of  the  creditor,  bond- 
holding,  salaried  classes,  who  bear  their  losses  silently 
behind  the  scenes;  secondly,  so-called  prosperity  is  often 
another  name  for  reckless  wastefulness,  for  which  there  must 
be  a  day  of  reckoning  in  the  form  of  a  commercial  crisis.* 

*  See  The  Gold  Supply  and  Prosperity,  edited  by  Byron  W.  Holt 
(The  Moody  Corporation),  New  York,  1907. 


CHAPTER   XV 

INDUCTIVE  VERIFICATION    (ECONOMIC) 
§    1 

In  the  last  chapter  we  found  statistical  evidence  of  the 
influence  of  changes  in  the  monetary  standard  upon  the 
rate  of  interest.  We  now  proceed  to  a  similar  inductive 
study  of  the  economic  —  as  distinct  from  the  monetary  — 
influences  upon  the  rate  of  interest. 

In  a  study  so  broad,  it  would  be  useless  to  attempt 
any  exhaustive  verification  by  statistics ;  the  facts  at  hand 
are  too  meager,  and  not  such  as  to  enable  us  to  isolate  the 
separate  causes  at  work.  It  will  usually  happen  in  any 
given  case  that  some  of  the  economic  causes  tending  to 
make  interest  high  are  combined  with  others  which  tend 
to  make  it  low.  The  fact,  therefore,  that  interest  is  either 
high  or  low  in  such  a  case  will  not,  of  itself,  be  decisive 
in  favor  of  any  theory.  The  best  that  we  can  expect  is  to 
show  that  the  facts  as  we  find  them  are  at  any  rate  consist- 
ent with  the  theory  maintained.  For  practical  purposes, 
such  a  showing  is  enough,  both  because  the  theory  should 
stand  on  its  own  merits  as  an  analysis,  without  the  bolster- 
ing of  statistical  verification;  and  because,  if  the  analysis 
were  really  incorrect,  a  very  cursory  examination  of  the 
facts  would  probably  suffice  to  refute  it. 

In  our  study  of  facts  it  is  well  to  remember  that  the  causes 
tending  to  make  interest  high  or  low  sometimes  work  out 
their  effects,  partly  or  wholly,  in  other  ways.  For  instance, 
the  economic  causes  which,  in  the  United  States,  have 
tended  to  make  interest  high,  have  also  tended  to  bring  in 
loans  from  other  countries,  such  as  Great  Britain,  where  the 
rate  of  interest  was  low.  The  introduction  of  the  loans 
prevented  interest  from  being  as  high  as  it  otherwise  would. 

u  289 


290  THE  RATE   OF  INTEREST  [Chap.  XV 

In  general  it  is  true  that  a  cause  which  would  tend  to 
make  interest  high  in  a  community  may  simply  result  in 
increasing  the  loans  contracted  by  that  community,  pro- 
vided there  exists  another  community  in  which  the  rate 
of  interest  is  lower.  If  recourse  to  borrowing  is  not  prac- 
ticable, other  methods  of  adding  to  present  at  the  ex- 
pense of  future  income  — of  ''tipping  forward"  the  income 
curve  —may  be  found.  If  this  "  tipping  forward"  goes  far 
enough  it  will  show  itself  in  a  dissipation  of  capital ;  if  not, 
in  a  slower  accumulation.  Contrariwise,  the  causes  which 
work  toward  lending  may,  if  lending  is  impracticable,  result 
in  some  other  form  of  "  tipping  back"  the  income  curve  and 
may  show  itself  in  a  more  rapid  accumulation  of  capital  or 
a  less  rapid  dissipation.  Finally,  the  same  economic  causes 
which  tend  to  make  interest  high  will  tend  also  to  encourage 
the  production  of  the  less  substantial  and  durable  instru- 
ments, whereas  those  causes  which  tend  to  make  interest 
low  will  favor  the  production  of  instruments  of  the  more 
durable  and  substantial  types. 

In  short,  in  our  collection  of  facts  we  should  ascribe 
very  similar  significance  to  the  four  sets  of  phenomena  — 
high  interest,  borrowing,  dissipation  of  capital,  and  perish- 
ability of  instruments;  any  causes  back  of  these  phenomena, 
which,  according  to  our  theory,  should  produce  any  one  of 
the  four,  will  tend  also  to  produce  the  other  three.  Like- 
wise we  should  ascribe  similar  significance  to  the  four  op- 
posing phenomena  — low  interest,  lending,  accumulation,  and 
durability  of  instruments. 

§  2 
Briefly  stated,  the  theory  we  are  testing  is  that  the  rate 
of  interest  expresses  human  preference  for  present  over 
future  goods,  as  that  preference  works  itself  out  from  the 
nature  of  the  individual  and  the  character  of  his  income- 
stream.  We  shall  begin  by  considering  the  manner  in 
which  the  nature  of  the  individual  influences  the  rate  of 
interest. 


Sec.  2]        INDUCTIVE  VERIFICATION   (ECONOxMIC)  291 

In  a  previous  chapter  we  enumerated  the  causes  which,  in 
the  nature  of  man,  tend  to  make  interest  high  or  low.  It 
was  there  maintained  that  foresight,  self-control,  and  regard 
for  posterity  tend  to  make  interest  low.  We  may  there- 
fore expect  to  find,  in  a  community  possessing  these  quali- 
ties, one  or  more  of  the  four  interequivalent  phenomena 
already  mentioned  — low  interest,  lending  to  other  com- 
munities, accumulation  of  capital,  and  construction  of  sub- 
stantial instruments ;  and  to  find,  in  a  community  lacking 
these  qualities,  one  or  more  of  the  four  opposite  conditions. 

No  extended  study  is  needed  to  show  that  precisely  these 
opposing  sets  of  phenomena  are  actually  found  in  the  two 
opposite  conditions  mentioned.  The  conmiunities  and 
nationalities  which  are  most  noted  for  the  qualities  men- 
tioned —  foresight,  self-control,  and  regard  for  posterity  — 
are  probably  Holland,  Scotland,  England,  France,  and  the 
Jews,  and  among  these  peoples  interest  has  been  low.  More- 
over, they  have  been  money  lenders,  they  have  the  habit 
of  thrift  or  accumulation,  and  their  instruments  of  wealth 
are  in  general  of  the  substantial  variety.  The  durability 
of  their  instruments  is  especially  obvious  in  their  buildings, 
both  public  and  private,  and  in  their  ways  of  transportation 
—  carriage  roads,  tramways,  and  railroads.  Thus  in  Eng- 
land the  railways  have  expended  an  average  of  $165,000 
per  mile,  which  is  from  two  to  three  times  the  corresponding 
expenditure  in  most  countries.^  The  difference,  though 
partly  explainable  by  a  difference  in  methods  of  account- 
ing, seems  largely  due  to  the  lower  rate  of  time-preference 
in  England. 

John  Rae  observes  of  Holland :  — 

"The  Dutch  seem,  of  all  European  nations,  hitherto  to  have  been 
inclined  to  carry  instruments  to  the  most  slowly  returning  orders. 
The  durability  given  to  all  the  instruments  constructed  by  them, 

*  See  Dorsey,  English  and  American  Railroads  Compared,  New 
York  (Wiley),  1887;  Price  Howell,  Journal  of  the  Royal  Statistical 
Society,  Vol.  LXII,  p.  83;  Commercial  and  Financial  Chronicle, 
Vol.  LXXIV,  p.  1224. 


292  THE   RATE  OF  INTEREST  [Chap.  XV 

the  care  with  which  they  are  finished,  and  the  attention  paid  to 
preserving  and  repairing  them,  have  been  often  noticed  by  travel- 
ers. In  tlie  days  when  their  industry  and  frugaUty  were  most 
remarkable,  interest  was  very  low,  government  borrowing  at  2 
per  cent.,  and  private  people  at  3."^ 

On  the  other  hand,  among  communities  and  peoples  noted 
for  lack  of  foresight  and  for  negligence  with  respect  to  the 
future  are  China,  India,  Java,^  the  negro  communities  in 
the  Southern  states,  the  peasant  communities  of  Russia,^ 
and  the  North  and  South  American  Indians,  both  before 
and  after  they  had  been  pushed  to  the  wall  by  the  white 
man.  In  all  of  these  communities  we  find  that  interest  is 
high,  that  there  is  a  tendency  to  run  into  debt  and  to  dissi- 
pate rather  than  accumulate  capital,  and  that  their  dwell- 
ings and  other  instruments  are  of  a  very  flimsy  and  perish- 
able character. 

It  may  well  be  that  there  are  other  causes  at  work  to 
produce  these  results.  We  are  here  merely  noting  the  fact 
that  lack  of  foresight  is  one  factor  present. 

Of  China,  Rae  states :  — 

"  The  testimony  of  travelers  ascribes  to  the  instruments  formed 
by  the  Chinese  a  durability  very  inferior  to  similar  instruments  con- 
structed by  Europeans.  The  walls  of  houses,  we  are  told,  unless 
of  the  higher  ranks,  are  in  general  of  unburnt  bricks  of  clay,  or  of 
hurdles  plastered  with  earth ;  the  roofs,  of  reeds  fastened  to  laths. 
We  can  scarcely  conceive  more  unsubstantial,  or  temporary  fabrics. 
Their  partitions  are  of  paper,  requiring  to  be  renewed  every  year. 

A  similar  observation  may  be  made  concerning  their  imple- 
ments of  husbandry  and  other  utensils.     They  are  almost  entirely 

'  The  Sociological  Theory  of  Capital,  pp.  128-129. 

^  My  colleague,  Professor  Clive  Day,  informs  me  that  the  rate 
of  interest  in  Java  is  often  40  per  cent. 

^  See  Bloch,  The  Future  of  War,  p.  205.  It  appears  that  the  peas- 
ant will  sell  a  promise  to  labor  a  short  time  in  the  future  at  one 
third  the  current  wages  I  See  also  E.  B.  Lanin  (pseud.),  "Russian 
Finance,"  Fortnightly  Review,  February,  1891,  Vol.  LV,  pp.  188,  190, 
196,  for  typical  and  extreme  cases  Inostranietz,  "  L'Usure  en  Russie," 
Journal  des  Economiste,  1893,  Ser.  5,  Vol.  XVI,  pp.  233-243,  states 
that  the  rates  paid  by  poor  peasants  to  well-to-do  peasants  are  fre- 
quently 5  per  cent,  per  week! 


Sec.  2]        INDUCTIVE  VERIFICATION   (ECONOMIC)  293 

of  wood,  the  metals  entering  but  very  sparingly  into  their  construc- 
tion ;  consequently  they  soon  wear  out,  and  require  frequent  re- 
newals." * 

"European  travelers  are  surprised  at  meeting  .  .  .  little  float- 
ing farms,  by  the  side  of  swamps  which  only  require  draining  to 
render  them  tillable.  It  seems  to  them  strange  that  labor  should 
not  rather  be  bestowed  on  the  solid  earth,  where  its  fruits  might 
endure,  than  on  structures  that  must  decay  and  perish  in  a  few 
years.  The  people  they  are  among  think  not  so  much  of  future 
years  as  of  the  present  time."  ^ 

"The  Father  Parennin,  indeed,  asserts,  that  it  is  their  great  de- 
ficiency in  forethought  and  frugality  in  this  respect,  which  is  the 
cause  of  the  scarcities  and  famines  that  frequently  occur.  'I  be- 
lieve,' he  says,  'that,  notwithstanding  its  great  number  of  inhabit- 
ants, China  would  furnish  enough  grain  for  all,  but  that  there  is 
not  sufficient  economy  observed  in  its  consumption,  and  that  they 
employ  an  astonishing  quantity  of  it  in  the  manufacture  of  the  wine 
of  the  country,  and  of  raque.'"  ^ 

"In  China,  we  are  told  by  Barrow,  that  the  legal  rate  of  interest 
is  12  per  cent.,  but  that,  in  reality,  it  varies  from  18  to  36."  * 

Simcox  writes  of  China  as  follows:  — 

"  The  legal  maximum  is  3  per  cent,  per  mensem,  and  the  usual 
rate,  as  already  mentioned,  30  per  cent.,  per  annum."  ^ 

Even  on  the  seacoast  where  Englishmen  have  settled, 
the  rate  of  interest  is  high,  and  its  reduction,  such  as  has 
occurred,  is  only  because  of  the  equivalent  economic 
phenomenon,  loans  from  abroad.  These  facts  are  seen  in  the 
Appendix,®  where  the  rates  of  interest  in  China  are  given. 
It  is  interesting  to  observe  how  the  economic  conditions 
in  China  which  at  first  produced  high  interest  afterward 
led  gradually  to  loans  from  England  and  a  fall  in  the  rate 
of  interest.  The  bank  rate  in  Shanghai  as  given  in  the  table 
was  at  first  (1866)  13  per  cent.,  and  gradually  fell  to  6  per 
cent,  as  investments  of  English  capitalists  were  made. 

*  The  Sociological  Theory  of  Capital,  pp.  88-89.       ^  Loc.  cit.,  p.  92. 
^  Loc.  cit.,  pp.  89-90.  ■•  Loc.  cit.,  p.  128. 

*  Primitive  Civilizations,  London  (Swan  Sonnenschein),  1894,  Vol. 
II,  p.  327. 

«  See  Appendix  to  Chap.  XIV,  §  1. 


294  THE  RATE  OF   INTEREST  [Chap.  XV 

Of  the  North  American  Indians,  Rae  observed :  — 

"Upon  the  banks  of  the  St.  Lawrence,  there  are  several  httle 
Indian  villages.  They  are  surrounded,  in  general,  by  a  good  deal 
of  land  from  which  the  wood  seems  to  have  been  long  extirpated 
and  have,  besides,  attached  to  them,  extensive  tracts  of  forest. 
The  cleared  land  is  rarely,  I  may  almost  say  never,  cultivated,  nor 
are  any  inroads  made  in  the  forest  for  such  a  purpose.  The  soil 
is,  nevertheless,  fertile,  and  were  it  not,  manure  lies  in  heaps  by 
their  houses.  Were  every  family  to  inclose  half  an  acre  of  ground, 
till  it,  and  plant  in  it  potatoes  and  maize,  it  would  yield  a  sufficiency 
to  support  them  one  half  the  year.  They  suffer  too,  every  now  and 
then,  extreme  want,  insomuch  that,  joined  to  occasional  intem- 
perance, it  is  rapidly  reducing  their  numbers.  This,  to  us,  so  strange 
apathy  proceeds  not,  in  any  great  degree,  from  repugnance  to  labor ; 
on  the  contrary,  they  apply  very  diligently  to  it,  when  its  reward 
is  immediate."  ' 

Of  the  South  American  Indians  in  Paraguay  Rae  tells 
of  the  difficulties  which  the  Jesuits  found  in  persuading 
the  natives  to  provide  for  the  future :  — 

"...  if  these  [the  Jesuits]  gave  up  to  them  the  care  of  the  oxen 
with  which  they  plowed,  their  indolent  thoughtlessness  would 
probably  leave  them  at  evening  still  yoked  to  the  implement. 
Worse  than  this,  instances  occurred  where  they  cut  them  up  for 
supper,  thinking,  when  reprehended,  that  they  sufficiently  excused 
themselves  by  saying  they  were  hungry."  ^ 

In  regard  to  the  negro  and  the  Russian  we  may  cite  the 
statistics  of  George  K.  Holmes  ^  and  the  observations  of 
N.  T.  Bacon." 

§  3 

In  many  if  not  all  of  the  cases  which  have  been  cited 
there  are,  of  course,  other  elements  which  would  tend 
to  explain  the  facts  besides  mere  mental  characteristics. 
Thus,  the  high  rate  of  interest  among  the  negroes  and  the 
Russian  peasants  is  undoubtedly  due  in  part  to  their  pov- 

'  The  Sociological  Theory  of  Capital,  pp.  71-72. 

*  Loc.  cit.,  p.  76.  3  Census  of  1890. 

*  Yale  Review,  Vol.  XII,  pp.  141,  239;   Vol.  XIII,  p.  51. 


Sec.  3]        INDUCTIVE  VERIFICATION   (ECONOMIC)  295 

erty,  though  their  poverty  is  in  turn  largely  due  to  the  men- 
tal characteristics.  There  is  here  in  operation  the  vicious 
circle  which  has  been  noted  in  Chapter  XII.  Where  there 
is  too  little  appreciation  of  the  needs  of  the  future,  capital 
tends  to  disappear;  and  the  pressure  of  poverty  tends  to 
enhance  still  further  the  demands  of  the  present  and  to 
press  down  its  victims  from  bad  to  worse. 

But  there  are  not  wanting  cases  in  which  even  persons  who 
have  wealth,  but  who  nevertheless  lack  foresight  and  self- 
control,  exhibit  the  same  facts,  especially  by  running  into 
debt.  This  is  characteristic  of  a  considerable  number  of 
the  spoiled  sons  of  rich  English  noblemen.  The  type  is  well 
described  in  some  of  Stevenson's  novels.  These  persons 
are  found  living  in  Australia  and  elsewhere  in  virtual 
exile  on  a  stipend  provided  by  their  families  at  stated 
intervals.  This  stipend  is  sometimes  provided  on  condition 
that  they  remain  away  from  their  original  environment  with 
its  temptations  to  extravagance.  One  such  individual 
known  to  the  writer  had  inherited  a  large  fortune.  The 
precaution  had  been  taken  to  leave  it  in  trust  so  that  he 
could  draw  only  the  income.  Yet  this  man  contrived  to 
contract  large  debts  on  chattel  mortgages  at  high  rates  of 
interest,  and  was  noted  for  his  wasteful,  short-sighted 
erection  of  temporary  dwellings  in  the  various  communities 
among  which  he  continually  flitted.  The  same  character- 
istics are  often  found  among  wealthy  students  at  univer- 
sities, who  have  acquired,  through  improper  home  training, 
an  exaggerated  idea  of  the  needs  of  the  moment  and  little 
appreciation  of  those  of  the  future.  These  men  become 
the  victims  of  money  lenders,  and  are  frequent  patrons  of 
the  pawn  shops. 

Not  only  do  we  find  examples  of  a  high  rate  of  preference 
for  present  over  future  goods  among  the  prodigally  rich, 
but  we  often  find  the  opposite  example  of  a  low  rate  of 
preference  for  present  over  future  goods  among  the  thrifty 
poor.  Examples  are  especially  frequent  among  the  Jews, 
whose  propensity  to  accumulate  and  to  lend  money  even 


296  THE  RATE  OF  INTEREST  [Chap.  XV 

in  the  face  of  misfortune  and  social  ostracism,  is  too  well 
known  to  require  extended  comment. 

§  4 

The  factor  which  has  been  designated  as  "  regard  for  pos- 
terity" deserves  special  attention.  Perhaps  the  most  con- 
spicuous example  of  extreme  disregard  for  posterity  is 
found  in  Rome  during  the  time  of  its  decline  and  fall.  The 
following  quotations  from  Rae  contain  important  testi- 
mony :  — 

"It  were  needless,"  he  says,  "to  enlarge  on  a  subject  so  well 
known  as  that  of  the  general  corruption  of  Roman  manners,  from 
the  time  of  the  first  Caesar.  VenaUty  and  licentiousness  may  be 
said  to  have  been  universal.  I  shall  confine  myself  to  one  particu- 
lar, as  marking  sufficiently  the  declension  of  those  principles  on 
which  the  strength  of  the  effective  desire  of  accumulation  mainly 
depends.  I  allude  to  the  decay  of  the  family  affections,  of  which 
evidence  everywhere  meets  us.  The  men  did  not  wish  to  be  fathers, 
scarcely  did  the  women  wish  to  be  mothers.  .  .  .  They  lived,  not 
in  others,  or  for  others,  but  for  themselves,  and  sought  their  good 
in  enjo}Tnents  altogether  selfish.  It  was  their  aim  to  expend  on 
their  own  personal  pleasures  whatever  they  possibly  could.  It 
would  seem  as  if  the  majority,  could  they  have  foreknown  the 
exact  limits  of  their  lives,  would  have  made  their  fortunes  and 
them  terminate  together.  As  they  could  not  do  so,  the  fortunes 
of  many  ended  before  their  lives,  as  the  fortunes  of  others  held  out 
beyond  their  lives.  To  reap,  however,  themselves,  while  alive, 
all  possible  benefit  from  what  they  might  chance  to  leave  others 
to  enjoy  after  their  death,  they  encouraged  some  of  the  members 
of  a  despicable  class  who  seem  to  have  constituted  no  inconsider- 
able part  of  Roman  society.  Parasites  ready  to  minister  to  every 
pleasure,  and  to  perform  every  possible  service,  waited  on  the  man 
of  wealth,  in  the  hope  and  expectation  of  enjoying  a  portion  of  it 
after  his  death.  They  were  more  desirable  than  children,  both 
because  they  were  able  to  give  something  more  than  mere  unsub- 
stantial affection  and  esteem,  and  because  they  were  willing  to 
give  it.  .  .  .  It  gave  occasion  to  the  law  compelling  parents 
to  leave  their  children  a  certain  part,  a  fourth,  of  their  property. 
Its  prevalence  may  be  judged  of  by  the  wording  of  the  enactments 
increasing  the  children's  share.  .  .  .  The  general  selfishness  of 
the  principles  guiding  the  conduct  of  individuals,  may  be  gathered 


Sec.  5]        INDUCTIVE  VERIFICATION   (ECONOMIC)  297 

from  the  prevailing  proverb,  "When  I  die  let  the  world  burn."  .  .  . 
Pasture  took  place  of  tillage  ;  corn  was  brought  from  the  provinces ; 
and  when  the  supply  failed  famine  ensued.  Even  the  construc- 
tion of  ships  for  the  transport  of  this,  and  other  merchandise,  would 
seem  to  have  been  an  effort  to  which  the  accumulative  principle 
was  scarcely  equal.  It  was  found  necessary  to  encourage  it  by 
rewarding  those  who  prosecuted  that  branch  of  industry.  Some- 
times land  formerly  cultivated  was  allowed  to  lie  entirely  waste, 
and  passed  altogether  out  of  the  class  of  instruments.  The  forest 
and  wilderness  gained  on  the  Romans,  as  they  would  now,  for 
similar  reasons,  on  an  Indian  population,  were  some  of  these  tribes 
put  in  possession  of  the  domains,  anciently  the  property  of  their 
race,  at  present  yielding  abundantly  to  the  provident  industry 
of  the  whites.  Had  there  been  no  interruption  of  the  barbarians, 
the  Empire  must  have  perished,  more  slowly  perhaps,  but  as  cer- 
tainly, from  the  operation  alone  of  these  internal  causes  of  decay. 
They  were  occasioning  a  progressive  diminution  of  the  capacity 
which  materials  formerly  possessed.  Thus,  it  is  to  the  Romans 
themselves  as  much  as  to  the  barbarians,  that  the  destruction  of 
the  public  edifices  is  to  be  ascribed.  The  stones  were  applied  to 
private  purposes."  ' 

"Thus,  among  the  Roman  writers,  the  heir  is  always  represented 
in  an  invidious  light,  and  to  save  for  him  is  represented  as  a  folly. 
The  writings  of  Horace,  and  the  contemporary  poets,  throughout, 
exemplify  the  prevalence  of  this  feeling."  ^ 

"  In  ancient  Rome,  interest  was  in  reality  exceedingly  high,  from 
12  to  50  per  cent."  ^ 

These  rates  doubtless  refer  to  the  degenerate  days. 
Previously,  at  the  time  of  the  end  of  the  repubhc,  the  rate 
was  as  low  as  4  to  6  per  cent.^ 

§  5 

The  characteristics  of  foresight,  self-control,  and  regard 
for  posterity  seem  to  be  partly  natural  and  partly  acquired 
within  the  lifetime  of  the  individual.     Among  the  cases 

'  Loc.  cit.,  pp.  95-99.  ^  Loc.  cit.,  p.  64. 

^  Loc.  cit.,  p.  129.  Rae's  authority  is  Boucher's  Histoire  de  U  Usure, 
Paris,  1819,  p.  2.5. 

■•  See  Seligman's  Principles  of  Economics,  New  York  (Longmans), 
1905,  p.  404. 


298  THE  RATE  OF  INTEREST  [Chap.  XV 

which  have  been  given  are  conspicuous  examples  of  both, 
although  it  is  difficult  here,  as  always,  to  disentangle  the 
influence  of  nature  from  that  of  environment.  We  are 
accustomed,  for  instance,  to  ascribe  to  the  Jews  a  natural 
racial  tendency  to  accumulate,  though  this  characteristic 
is  certainly  reenforced  by,  if  not  entirely  due  to,  the  ex- 
traordinary influence  of  Jewish  tradition.  Of  the  Scotch, 
it  would  be  difficult  to  say  how  much  of  their  thrift  is  due 
to  nature  and  how  much  to  training  handed  down  from 
father  to  son.  The  American  negro  is  regarded  by  nature 
as  a  happy-go-lucky  creature ;  but  recent  experience  with 
industrial  schools  has  demonstrated  the  fact  that  these 
characteristics  can  be  largely  reversed  by  training,  if  in 
fact  they  have  not  been  entirely  created  by  the  lack  of 
training  under  conditions  of  slavery.  There  is  now  ac- 
cumulating much  testimony  ^  to  show  that  there  is  more 
error  than  truth  in  the  common  opinion  as  to  the  relatively 
great  importance  of  heredity  as  compared  with  environ- 
ment. 

When  postal  savings  banks  were  first  introduced  in  Eng- 
land, it  was  objected  that  the  habits  of  the  English  poor,  for 
whom  they  were  intended,  were  such  that  they  would  never 
make  use  of  them.  But  Gladstone  insisted  that  habits 
were  an  arbitrary  matter,  and  that  the  fashion  of  spending 
could  be  displaced  by  the  fashion  of  saving  as  soon  as  the 
principle  of  imitation  had  had  time  to  operate.  The  ex- 
perience with  English  postal  savings  banks  has  justified 
his  prediction.^ 

In  fact,  it  would  be  a  serious  mistake  to  assume  that  the 
characteristics  of  man  as  to  foresight,  self-control,  and  regard 
for  his  own  and  his  children's  future  are  fixed  racial  or 
national  qualities.     The  part  which  nature  may  play  in 

*  For  instance,  the  reports  of  the  Children's  Aid  Society  of  New 
York;  the  child-saving  work  of  Dr.  and  Mrs.  J.  H.  Kellogg  at  Battle 
Creek;  the  evidence  of  the  British  Interdepartmental  Committee 
on  School  Children,  etc. 

^  See  The  Development  of  Thrift,  by  Mary  W.  Brown,  New  York 
(Macmillan),   1900. 


Sec.  6]        INDUCTIVE  VERIFICATION   (ECONOMIC)  299 

these  matters  is  as  yet  far  from  being  understood;  but 
however  great  that  part  may  be,  it  is  certainly  true  that 
the  influence  of  training  is  also  great,  and  therein  lies  the 
possibility  and  hope  of  social  reform  in  these  matters.  It 
should  be  one  of  the  distinct  aims  of  any  intelligent  modern 
education,  whether  in  the  home  or  the  school,  to  inculcate 
foresight,  self-control,  and  a  due  regard  for  the  needs  of 
future  years  and  even  of  future  generations.  It  goes  with- 
out saying  that  individuals  and  nations  with  these  char- 
acteristics have  therein  a  more  secure  and  permanent  claim 
for  success  in  all  directions. 


§  6 

But,  as  has  been  emphasized  in  previous  chapters,  the  rate 
of  preference  for  present  over  future  goods  is  not  a  ques- 
tion of  mere  personal  characteristics,  but  depends  also  upon 
the  character  of  one's  income-stream;  namely,  on  its  size, 
shape,  composition,  and  probability.  In  respect  to  size,  our 
theory  maintains  that  the  larger  the  income,  other  things  such 
as  foresight  and  self-control  being  equal,  the  lower  the  rate  of 
preference  for  present  over  future  goods.  If  this  is  true,  we 
should  expect  to  find  poverty  and  riches  associated  re- 
spectively with  a  high  and  a  low  rate  of  interest,  or  with 
borrowing  and  lending,  or  with  spending  and  saving,  or 
with  perishable  and  durable  instruments.  That  this  char- 
acterization is  in  general  correct  is  not  likely  to  be  denied. 
It  is  true  of  course  that  the  amount  loaned  to  the  poor  is 
small  because  each  individual  loan  is  necessarily  small ;  but 
the  number  oi  these  loans  is  very  great,  and  the  desire  of  the 
poor  to  borrow,  when  it  exists,  is  very  intense.  The  many 
conspicuous  exceptions  to  these  rules  are  explainable  on 
other  grounds.  It  not  infrequently  happens  that  the  poor, 
instead  of  being  borrowers,  are  lenders;  but  in  this  case 
either  they  have  unusual  foresight,  self-control,  regard  for 
their  children,  and  other  qualities  tending  in  the  same  direc- 
tion, or  else  their  income-stream  has  such   a   time-shapo 


300  THE  RATE  OF   INTEREST  [Chap.  XV 

as  to  encourage  lending  rather  than  borrowing.  Reverse 
conditions  apply  likewise  to  the  case  of  many  wealthy  men, 
viz.  those  who  are  borrowers  rather  than  lenders.  Whether 
from  wrong  training  or  other  causes,  they  lack  foresight,  seK- 
control,  regard  for  posterity,  etc.  But  disregarding  these 
factors  and  confining  our  view  to  the  direct  influence  of  the 
size  of  income,  it  is  true,  in  a  general  way,  that  the  poor 
are  more  eager  borrowers  than  the  rich,  and  will  often  pat- 
ronize pawn  shops  and  other  agencies  in  which  the  rate 
of  interest  is  inordinately  high;  also  that  their  dwellings 
or  other  structures  are  often  of  a  very  unsubstantial  char- 
acter, such  as  would  not  ''pay"  except  to  those  who  put 
a  very  high  estimate  on  present  as  compared  with  future 
goods.  The  deeper  the  poverty,  the  higher  the  rates  which 
the  borrowers  are  compelled  to  accept.  Even  pawn- 
broking  is  not  available  for  the  extremely  poor,  but  is 
patronized  rather  by  the  moderately  poor.  Those  who  are 
extremely  poor  cannot  give  the  kind  of  security  which  the 
pawnbroker  requires.  On  this  account  they  become  the 
victims  of  even  higher  rates  of  interest,  pledging  their 
stoves,  tables,  beds,  and  other  household  furniture  for  the 
loans  they  contract.  Tliese  loans  are  repaid  in  installments 
such  that  the  rate  of  interest  is  seldom  lower  than  100  per 
cent,  per  annum. ^ 

Turning  from  classes  to  countries,  it  is  noteworthy  that 
in  the  countries  in  which  there  are  large  incomes  we  find  low 
interest,  a  tendency  to  lend  rather  than  borrow,  accumulate 
rather  than  spend,  and  to  form  durable  rather  than  perish- 
able instruments,  whereas  in  countries  where  incomes  are 
low  the  opposite  conditions  prevail.  Thus,  incomes  are 
large  and  interest  is  low  in  Holland,  France,  and  England, 
whereas  the  reverse  conditions  hold  in  Ireland,  China,  India, 
and  the  Philippines.     In  Ireland,  for  instance,  especially 

*  For  details  as  to  thirteen  typical  loans  of  this  character,  see 
U.  S.  Bureau  of  Labor  Bulletin,  No.  64,  May,  1906,  pp.  622-633. 
Thus,  "loan  1,"  143  per  cent.,  "loan  3,"  224  per  cent.,  "loan  7,"  156 
per  cent. 


Sec.  7]        INDUCTIVE  VERIFICATION   (ECONOMIC)  301 

in  the  early  part  of  the  nineteenth  century,  the  rate  of 
interest  was  high.  The  cottier  was  always  in  debt,  and  his 
hut  and  other  instruments  were  of  the  most  unsubstantial 
variety.^  Again  in  the  Philippines  the  rates  of  interest 
on  good  security  are  often  2,  5,  and  even  10  per  cent,  a 
month.  ''The  Chinese  money  lender  frequently  takes 
advantage  of  the  Filipino's  poverty."^  Many  of  these 
cases  may  be  wholly  or  partly  explained  by  other  causes 
such  as  have  been  mentioned  in  the  last  section.  The 
possibility  of  more  than  one  explanation  shows  that  in  this 
field  we  can  scarcely  hope  to  adduce  any  complete  proof 
of  an  inductive  nature.  But  since  any  of  the  possible 
explanations  fit  in  with  our  theory,  we  are  safe  in  saying 
that  the  facts  do  not  at  any  rate  contradict  that  theory. 


§  7 

As  to  the  influence  of  the  composition  of  income,  it  is 
even  more  difficult  to  obtain  any  statistical  confirmation  of 
value.  In  a  previous  chapter  it  was  shown  that  variations 
in  the  amount  of  that  income  which  takes  the  form  of  food 
would  have  an  effect  on  the  rate  of  interest  similar  to  the 
effect  of  variations  in  the  total  income  itself.  Scarcity 
of  food  should  therefore  cause  high  interest,  and  abun- 
dance of  food,  low  interest.  Certain  presumptive  evidence 
is  found  in  the  observation  of  Jevons  on  the  relation  be- 
tween the  price  of  wheat  and  the  rate  of  discount.^  Wheat 
being  the  most  typical  food  in  England,  it  may  be  assumed 
with  considerable  probability  that  its  price  varies  inversely 
with  the  amount  of  food  consumed.     Jevons  found  that  a 

>  See  Longfield,  "The  Tenure  of  Land  in  Ireland,"  in  Proloyn's 
Systems  of  Land  Culture,  London  (Cassell,  Petter,  and  Galpin),  1876, 
p.  16. 

2  From  a  letter  to  the  author  from  Professor  E.  W.  Kemmerer;  see 
also  his  article  in  The  Business  Monthly,  Pittsburg,  April,  1907,  p.  2. 

^  See  Investigations  in  Currency  and  Finance,  1884,  p.  xiv;  also, 
Robert  Goodbody,  in  Byron  W.  Holt's  Gold  Supply  and  Prosperity, 
p.  166. 


302  THE  RATE  OF  INTEREST  [Chap.  XV 

high  price  of  wheat  corresponded  to  high  rates  of  interest, 
and  vice  versa.  This  would  ahnost  amount  to  saying  that  a 
relative  scarcity  of  food  was  associated  with  high  interest, 
and  vice  versa.  During  the  siege  of  Paris  the  rate  of  inter- 
est was  high,  although  other  causes  than  the  scarcity  of 
bread  were  doubtless  accountable  for  the  fact. 


§  8 

As  to  the  influence  of  risk,  we  encounter  similar  diffi- 
culties. But  evidence  as  to  our  main  contention,  namely, 
that  in  general  risk  tends  to  raise  the  commercial  rate  of 
interest  but  to  lower  pure  interest,  is  forthcoming.  The 
first  part  of  this  proposition  is  a  matter  of  so  common  ob- 
servation that  no  special  collection  of  facts  is  necessary. 
Every  lender  or  borrower  knows  that  the  rate  of  interest 
varies  directly  with  risk.  A  bird  in  the  hand  is  worth 
two  in  the  bush.  The  principle  applies  not  only  to  the 
explicit  interest  in  loan  contracts,  but  to  the  implicit 
interest  which  goes  with  the  possession  of  all  capital. 
Where  there  is  uncertainty  whether  capital  saved  for  the 
future  will  ever  be  of  service,  but  there  is  certainty  that 
it  can  be  of  service  if  used  immediately,  the  possessor 
needs  the  possibility  of  a  very  high  future  return  in  order 
to  induce  him  to  save  the  capital  for  future  use.  It  is  note- 
worthy that  in  time  of  war  there  is  a  ruthless  destruction 
of  crops  and  a  tendency  among  the  possessors  of  consumable 
wealth  to  enjoy  it  while  they  may.  The  same  conditions 
are  characteristic  of  communities  which  are  in  a  perpetual 
state  of  uncertainty.^  "  The  rate  of  interest  is  everywhere 
proportional  to  the  safety  of  investment.  For  this  reason 
we  find  in  Korea  that  a  loan  ordinarily  brings  from  2  to 
5  per  cent,  per  month.  Good  security  is  generally  forth- 
coming, and  one  may  well  ask  why  it  is  so  precarious  to 

'  On  the  uncertainties  of  Indian  life,  see  The  Sociological  Theory 
of  Capital,  pp.  69,  70. 


Sec.  8]        INDUCTIVE  VERIFICATION   (ECONOMIC)  303 

lend.  The  answer  is  not  creditable  to  Korean  justice. 
...  In  a  land  where  bribery  is  almost  second  nature, 
and  private  rights  are  of  small  account  unless  backed  up 
by  some  sort  of  influence,  the  best  apparent  security 
may  prove  a  broken  reed  when  the  creditor  comes  to  lean 
upon  it."  ^ 

There  remains  the  second  part  of  the  proposition  in  re- 
gard to  risk ;  namely,  that  while  risk  tends  to  increase  the 
rate  of  interest  on  risky  loans,  it  tends  at  the  same  time  to 
decrease  that  on  safe  loans.  This  proposition  is  not  familiar 
to  most  persons.  It  has  usually  caused  surprise  when, 
during  a  time  of  political  stress  and  danger,  the  rates  of 
interest  on  perfectly  safe  loans  were  found  to  be  so  small. 
Many  such  instances  may  be  cited.  At  certain  periods 
during  the  Civil  War,  when  the  greatest  uncertainty 
prevailed,  loans  with  good  security  were  contracted  at 
nominal  rates,  and  bank  deposits  tended  to  accumulate 
for  lack  of  sufficient  outlet  in  secure  investments.  Times 
when  public  confidence  is  shaken  are  characterized  not  only 
by  high  rates  on  unsafe  loans,  but  by  efforts  on  the  part 
of  timid  investors  to  find  a  safe  place  for  their  savings,  even 
if  they  have  to  sacrifice  some  or  all  of  the  interest  upon  it. 
They  will  even  hoard  it  in  stockings  and  safe  deposit  vaults, 
or  leave  it  idle  on  deposit  in  bank.  " .  .  .  In  1903  .  .  . 
the  public  took  alarm  and  began  to  hoard  their  capital 
in  the  form  of  banking  credits,  instead  of  bidding  with  it 
for  securities.  In  the  meantime,  the  scarcity  of  free  capital 
in  the  market  enabled  the  banks,  which  held  the  money 
of  the  pubfic,  to  exact  5  and  6  per  cent."  ^  We  may  even 
occasionally  find  cases  in  which  the  desire  to  obtain  a  safe 
method  of  using  capital  is  so  keen  and  so  difficult  to  satisfy 
that  the  rate  of  interest  is  negative.  The  investor  is  then 
in  the  position  of  the  user  of  a  safe  deposit  vault,  thankful 
enough  to  receive  the  assurance  that  his  capital,  by  being 

»  H.  B.  Hurlbert,  The  Passing  of  Korea,  New  York,  1906,  p.  283. 
2  Charles  A.  Conant,  "How  the  Stock    Market    reflects  Values," 
North  American  Review,  March,  1905,  pp.  346-359. 


304  THE  RATE  OF  INTEREST  [Chap.  XV 

intrusted  to  another,  will  not  be  diminished,  to  say  noth- 
ing of  being  increased/ 

§  9 

We  still  need  to  verify  the  most  essential  part  of  our 
theory ;  namely,  that  the  rate  of  interest  depends  upon  the 
time-shape  of  the  income-stream.  If  the  theory  is  correct, 
we  should  find,  other  things  being  equal,  that  when,  in  any 
community,  the  income-streams  of  its  inhabitants  are  in- 
creasing, the  rate  of  interest  will  be  high ;  that  when  they 
are  decreasing,  the  rate  of  interest  will  be  low;  and  that 
when  they  alternate  from  one  condition  to  the  other,  the 
rate  of  interest  will  also  alternate  according  to  the  period  of 
the  loan. 

The  most  striking  examples  of  increasing  income-streams 
are  found  in  new  countries.  It  may  be  said  that  the  United 
States  has  almost  always  belonged  to  this  category.  Were 
it  possible  to  express  by  exact  statistics  or  diagrams  the 
size  of  American  incomes,  they  would  undoubtedly  show  a 
steady  increase  since  colonial  days.  Statistics  almost  equiv- 
alent to  these  desiderata  are  available  (though  not  very  accu- 
rate) in  the  form  of  the  United  States  Census  figures  of 
"per  capita  wealth,"  as  well  as  statistics  of  production  and 
consumption  of  staple  commodities  and  of  exports  and  im- 
ports. These,  combined  with  common  observation  and 
the  statements  of  historians,  lead  to  the  conclusion  that 
American  incomes  have  been  on  the  increase  for  two  hun- 
dred years.  It  is  also  true  that  during  this  period  of 
rising  incomes,  the  rate  of  interest  has  been  high.  The 
simplest  interpretation  of  these  facts  is  that  Americans, 
being  constantly  under  the  influence  of  great  expectations, 
have  been  always  ready  to  promise  a  relatively  large  part 
of  their  abundant  future  income  for  a  relatively  small  ad- 
dition to  their  present,  just  as  he  who  expects   soon   to 

*  SeeBagehot,  Lombard  Street,  Chap.  VI;  also,  Macaulay,  History  of 
England,  Chap.  XIX. 


Sec.  9]        INDUCTIVE  VERIFICATION   (ECONOMIC)  305 

come  into  a  fortune  wishes  to  anticipate  its  realization  by 
contracting  a  loan. 

Not  only  has  the  rate  of  interest  been  high  in  America 
as  compared  with  other  countries  during  this  period  of  as- 
cending incomes,  but  some  of  the  other  conditions  equiva- 
lent to  a  high  rate  of  interest  have  also  been  in  evidence. 
Thus,  the  country  has  been  conspicuously  a  borrowing 
country,  in  debt  to  other  countries.  The  proceeds  of 
such  loans  have  shown  themselves  in  increased  imports 
and  diminished  exports,  creating  a  so-called  unfavorable 
balance  of  trade.  These  phenomena  have  usually  been 
expressed  as  a  ''demand  for  capital" ;  but,  while  it  is  quite 
true  that  the  exploitation  of  our  natural  resources  required 
the  construction  of  railways  and  other  forms  of  capital, 
this  fact  is  better  and  more  fully  expressed  in  terms  of  in- 
come. We  wanted,  not  the  railways  and  machinery  them- 
selves, but  the  future  enjoyable  products  to  which  this 
apparatus  led.  The  construction  of  these  instruments 
necessarily  diminished  the  immediate  enjoyable  income 
of  the  country  and  added  to  that  of  the  expected  future. 
It  was  to  even  up  this  disparity  of  immediate  and  remote 
income  that  loans  were  contracted.  It  does  not  matter 
whether  the  loans  from  the  foreigner  were  received  in  the 
form  of  machinery  and  other  instruments  of  production,  or 
in  the  form  of  the  comforts  of  life  to  support  us  while  we 
ourselves  constructed  the  instruments.  In  either  case  the 
essential  fact  is  the  transformation  of  the  income-stream, 
and  not  the  ''need  of  capital,"  which  is  merely  one  of  the 
means  thereto.  Import  statistics  show  that,  as  a  matter 
of  fact,  we  received  our  loans  from  the  foreigner  in  both 
forms. 

Not  only  have  we  witnessed  the  phenomena  of  high  rates 
of  interest  and  of  borrowing  during  this  period  of  American 
development,  but  it  is  also  true  that  the  character  of  the 
instruments  created  was  for  the  most  part  of  the  unsub- 
stantial and  "quickly  returning"  kinds.  Our  highways, 
as  John  Rae  pointed  out,  were  little  more  than  the  natural 


306  THE  RATE  OF  INTEREST  [Chap.  XV 

surface  of  the  earth  after  the  removal  of  trees  and  rocks; 
our  railwa3^s  were  Hghtly  ballasted,  often  '' narrow  gauge," 
and  crooked  to  avoid  the  necessity  of  excavations  and  tun- 
nels; our  earliest  buildings  were  rude  and  unsubstantial. 
Everything  was  done,  not  in  a  permanent  manner  with 
reference  to  the  remote  future,  but  in  order  to  save  a  large 
first  cost. 

During  the  last  two  decades  these  conditions  have  been 
reversed.  The  rates  of  interest  in  America  have  fallen 
greatly,  as  the  statistics  in  the  Appendix  will  show.^  We 
have  ceased  to  be  a  borrowing  nation,  and  are  buying 
back  our  securities  from  abroad.  This  repayment  of  debts 
is  accomplished  through  the  export  of  our  now  abundant 
products,  and  creates  a  so-called  favorable  balance  of  trade. 
Again,  the  character  of  the  instruments  which  have  been 
now  for  some  time  in  process  of  construction  is  of  the  most 
substantial  kind.  Steel  rails  have  long  since  taken  the  place 
of  iron  rails,  ''broad  gauge"  of  "narrow  gauge";  railways 
have  been  straightened  by  expensive  tunnels,  by  bridges, 
and  by  excavations ;  ^  dwellings  and  other  buildings  have 
been  made  more  substantial;  macadamized  roads  are 
gradually  coming  into  vogue ;  and  in  every  direction  — 
industrial,  agricultural,  and  domestic  — there  is  an  evident 
tendency  to  invest  a  large  first  cost  in  order  to  reduce  future 
running  expenses. 

§  10 

Thus  in  America  we  see  exemplified  on  a  very  large  scale 
the  truth  of  the  theory  that  a  rising  income-stream  raises 
and  a  falling  income-stream  depresses  the  rate  of  interest, 
or  that  these  conformations  of  the  income-stream  work  out 
their  effects  in  other  equivalent  forms.  A  similar  causation 
may  be  seen  in  particular  localities  in  the  United  States,  es- 

*  See  Appendix  to  Chap.  XIV,  §  1. 

*  It  is  estimated  that  Western  railways  in  the  United  States  have 
actually  under  way  or  in  contemplation  improvements  amounting 
to  $1,000,000,000.     Wall  Street  Journal,  December  19,  1905. 


Sec.  10]      INDUCTIVE  VERIFICATION  (ECONOMIC)  307 

pecially  where  changes  have  been  rapid,  as  in  mining  com- 
munities. In  California,  in  the  two  decades  between  1850 
and  1870,  following  the  discovery  of  gold,  the  income-stream 
of  that  state  was  increasing  at  a  prodigious  rate,  while  the 
state  was  isolated  from  the  world,  railroad  connection  with 
the  East  not  being  completed  until  1869.  During  this 
period  of  isolation  and  ascending  income,  "...  oppor- 
timities  for  investment  were  innumerable.  Hence  the 
rates  of  interest  were  abnormally  high.  The  current  rates 
in  the  '  early  days '  were  quoted  at  1|^  to  2  per  cent,  a  month. 
.  ,  .  The  thrifty  Michael  Reese  is  said  to  have  half  repented 
of  a  generous  gift  to  the  University  of  California,  with  the 
exclamation,  'Ah,  but  I  lose  the  interest,'  a  very  natural 
regret  when  interest  was  24  per  cent,  per  annum."  ^  After 
railway  connection  in  1869,  Eastern  loans  began  to  flow  in. 
The  decade,  1870-1880,  was  one  of  transition  during  which 
the  phenomenon  of  high  interest  was  gradually  replaced 
by  the  phenomenon  of  borrowing  from  outside.  The  rate 
of  interest  consequently  dropped  from  11  per  cent,  to  6 
per  cent.^  ''Since  1880  the  economic  history  of  California, 
or  at  least  of  San  Francisco  and  vicinity,  has  not  differed 
so  very  much  from  that  of  the  rest  of  the  country."  ' 
During  recent  years  the  rate  on  mortgages  in  San  Francisco, 
up  to  the  time  of  the  earthquake  and  fire,  has  been  4  to  4 J 
per  cent,  exclusive  of  the  state  tax. 

The  same  phenomena  of  enormous  interest  rates  were 
also  exemplified  in  Colorado  and  the  Klondike.  There 
were  many  instances  in  both  these  places  during  the  tran- 
sition period  from  poverty  to  affluence,  when  loans  were 
contracted  at  over  50  per  cent,  per  annum,  and  the  bor- 
rowers regarded  themselves  as  lucky  to  get  rates  so  "low." 
It  was  also  conspicuously  true  that  the  first  buildings  and 
apparatus  constructed  in  these  regions  were  very  unsub- 

'  Carl  C.  Plehn,  "Notes  concerning  the  Rates  of  Interest  in  Cali- 
fornia," Quarterly  Publications  of  the  American  Statistical  Associa- 
tion, September,  1899,  pp.  351-352. 

*  Ibid.,  p.  353.  '  Ibid.,  p.  353. 


308  THE  RATE   OF   INTEREST  [Chap.  XV 

stantial.  Rude  board  cabins  were  put  up  in  a  day.  Thus, 
high  interest,  borrowing,  and  unsubstantial  capital  were  the 
phenomena  which  attended  these  communities  when  under- 
going their  rapid  expansion. 

In  Nevada  in  the  seventies,  when  the  mines  were  in- 
creasing their  product  and  the  income  of  its  inhabitants  was 
tending  upwards,  the  rate  of  interest  was  high  and  the 
people  in  debt.  The  bonded  state  debt  itself  amounted  to 
$500,000  and  drew  15  per  cent,  interest.^  In  the  next  dec- 
ade all  these  conditions  were  reversed.  The  mines  were 
on  the  decline,^  the  rate  of  interest  fell,  and  the  state  and 
territorial  debts  were  largely  paid  off.^  The  fall  of  the  rate 
of  interest  in  this  case  could  not  have  been  due  to  the  in- 
troduction of  loans  from  outside,  except  so  far  as  old  debts 
were  refunded  at  lower  rates;  fresh  loans  were  seldom 
made,  as  the  state  had  ceased  to  be  a  good  place  for  new 
investments.  In  the  last  few  years  new  Nevada  mines 
in  the  gold-field  region  have  been  opened.  Loans  are  again 
entering  the  state,  and  the  same  cycle  of  history  as  above 
described  is  about  to  be  repeated. 

Lumbering  communities  often  go  through  a  somewhat 
similar  cycle.  The  virgin  forests  when  first  attacked  tend 
to  increase  rapidly  the  income-streams  of  those  who  exploit 
them.  Then  comes  a  period  of  decrease.  Thus  in  Michigan 
two  or  three  decades  ago  the  lumber  companies  found  a 
profitable  investment,  and  borrowed  in  order  to  exploit  the 
Michigan  forests.  After  the  exploitation  was  complete 
and  the  forests  had  been  (often  unwisely)  exhausted,  those 
regions  ceased  to  be  a  desirable  place  for  investment,  and 
their  owners  came  into  the  position,  not  of  receiving,  but 
of  seeking,  investments. 

After  the  trunk  lines  of  railway  were  completed,  connect- 
ing the  Mississippi  Valley  with  the  East,  there  arose  a  great 
demand  for  loans  to  exploit  the  rich  farming  lands  in  that 

1  See  "Message  of  the  Governor  of  the  State  of  Nevada,"  1879. 
^  Mines  and  Quarries,  1902.     Special  Report  U.  S.  Census,  p.  255. 
^  See  later,  "Messages  of  the  Governor  of  the  State  of  Nevada." 


Sec.  11]      INDUCTIVE  VERIFICATION   (ECONOMIC)  309 

section  of  the  country.  The  rate  of  interest  frequently  was 
10  and  12  per  cent.,  and  even  higher.  During  much  of  this 
time  the  Northwestern  Mutual  Life  Insurance  Company, 
up  to  1880,  made  an  average  rate  on  all  its  mortgage 
loans,  $10,000,000  in  amount,  of  nearly  10  per  cent. 
Another  striking  proof  of  the  demand  for  loans  in  the 
Middle  West  is  shown  in  the  experience  of  the  New  York 
and  Connecticut  life  insurance  companies.  New  York, 
up  to  1880,  had  a  law  prohibiting  the  life  insurance  com- 
panies in  that  state  from  loaning  on  real  estate  outside  of 
New  York.  Connecticut  had  no  restriction  in  this  regard, 
and  her  companies  loaned  extensively  in  the  West.  The 
result  is  seen  in  the  rates  of  interest  realized  on  mortgage 
loans  of  companies  in  the  two  states.  Taking  the  period 
1860  to  1880  as  a  whole,  the  Connecticut  companies  reaUzed 
l^Q  per  cent,  more  than  did  the  New  York  companies. 
Since  1880,  the  Middle  West  has  developed  rapidly,  and 
loans  on  farming  lands  are  now  made  at  low  rates.  During 
the  past  two  years,  certain  of  the  insurance  companies  have 
been  making  mortgage  loans  in  Illinois  at  4^  per  cent.* 
A  similar  history  has  recently  been  enacting  itself  in  the 
northwest  region  of  the  United  States.  During  the  period 
of  exploitation  while  the  Great  Northern  and  other  railways 
were  developing  this  territory,  the  phenomena  of  high 
interest  and  borrowing  were  almost  universal.  But  lat- 
terly, much  to  the  surprise  of  many  Easterners,  it  has  been 
found  that  the  rates  of  interest  in  these  states  have  been 
at  times  lower  even  than  in  most  American  cities,  and  that 
the  inhabitants  have  actually  been  seeking  to  lend  to  the 
East  instead  of  to  borrow  from  it. 


§  u 

Australia  furnishes  another  example  of  a  country  which, 
through   improvement   in   the   means   of   transportation, 

'  See    Zartman,    The    Investments   of   Life    Insurance   Companies, 
New  York  (Holt),  1906,  pp.  89-91. 


310  THE  RATE  OF  INTEREST  [Chap.  XV 

created  a  great  demand  for  loans.  The  rate  during  the 
fifties  on  safe  securities  was  rather  low.  This  rate  increased 
until,  during  the  seventies,  7,  8,  and  9  per  cent,  were  usual. 
Since  1880  the  rates  have  declined.^ 

England  may  perhaps  be  cited  as  exemplifying  the  same 
phenomena  which  we  have  seen  in  the  case  of  Nevada, 
though  in  a  less  degree.  Thus,  as  Nevada  has  exhausted 
its  mines  of  precious  metals,  so  England  is  on  the  road 
toward  exhaustion  of  its  coal  and  iron  supplies.  Tliis  fact 
has  been  noted  with  considerable  alarm  by  many  econo- 
mists, especially  Jevons.  It  does  not  necessarily  indicate 
that  the  economic  power  of  Englishmen  will  be  greatly  or 
even  at  all  lessened.  Its  significance  shows  itself  in  the 
tendency  of  England  to  become  an  investing  country.  It 
is  the  part  of  those  who  have  property  in  mines  not  to  use 
all  of  the  product  as  income,  but  to  reinvest  in  order  to 
maintain  the  capital.  This  the  Englishmen  have  done  and 
are  doing;  and  being  unable  to  make  satisfactory  invest- 
ments at  home,  they  have  placed  their  loans  all  over  the 
world.  The  income-stream  produced  for  them  by  their 
native  island  is  destined,  perhaps,  to  decline,  certainly 
not  greatly  to  increase;  but  by  saving  from  this  declining 
income  and  investing  in  South  America,  Australia,  South 
Africa,  and  other  regions  where  the  natural  resources  are  on 
the  increase  instead  of  on  the  wane,  the  Englishmen  may 
still  maintain  their  capital  intact  or  even  increase  it.  It 
is  said,  with  how  much  accuracy  I  do  not  know,  that 
Englishmen  own  an  area  in  the  United  States  as  large  as 
Ireland.  The  figures  given  by  Giffen  show  that  the  na- 
tional income  increased  for  several  decades,  but  that  the 
rate  of  increase  slackened  ^  for  the  decade  1875-1885  com- 
pared with  1865-1875 ;  that  whereas  in  the  earlier  decades 
there  was  a  general  increase  in  all  directions,  in  the  later 

'  Zartman,  The  Investments  of  Life  Insurance  Companies,  p.  103. 

2  Giffen,  Growth  of  Capital,  London  (Bell),  1889.  See  also  articles 
by  GifiFen  in  continuation  of  the  same  subject  in  Journal  of  Royal  Sta- 
tistical Society. 


Sec.  12]      INDUCTIVE  VERIFICATION   (ECONOMIC)  311 

decade  there  were  many  items  of  decrease/  the  most  nota- 
ble being  of  mines  and  ironworks ;  '  and  finally,  that  among 
the  greatest  increases  was  that  of  foreign  investments.^ 

We  thus  see  that  the  rate  of  preference  for  present  over 
future  goods,  in  its  various  manifestations  —  such  as  a  high 
or  low  rate  of  interest,  more  or  less  lending  and  accumu- 
lation of  capital,  and  the  character  of  the  instruments 
formed  —  depends  upon  the  time-shape  of  the  income-stream 
of  a  community,  as  determined  by  its  natural  resources; 
that  in  virgin  countries  like  the  United  States  in  the  last 
two  centuries,  Australia  and  South  Africa,  rich  in  timber, 
untouched  ore,  and  raw  materials  generally,  the  income- 
stream  is  of  the  ascending  type  and  produces  a  high  rate 
of  preference,  whereas  in  older  countries  like  England  and 
Holland,  in  which  the  natural  resources  have  been  fully 
developed,  and  are  even  declining,  the  rate  of  preference 
tends  to  be  low ;  such  a  country  either  uses  up  its  income 
and  thereby  reduces  its  capital,  or  seeks  economic  salvation 
in  foreign  investment. 

§  12 

The  time-shape  of  an  income-stream  is,  however,  deter- 
mined in  part  by  other  causes  than  natural  resources. 
Among  these  causes,  misfortune  holds  a  high  place  in 
causing  temporary  depressions  in  the  income-stream,  that 
is,  giving  to  it  a  time-shape  which  is  first  descending  and 
afterwards  ascending.  The  effect  of  such  temporary 
depression  is  to  produce  a  high  valuation  of  immediate 
income  during  the  depression  period  as  compared  with  the 
valuation  of  the  income  expected  after  the  depression  is 
over.  It  is  a  matter  of  common  observation  in  private  life 
that  loans  often  find  their  source  in  personal  misfortune. 
The  above-mentioned  investigation  of  the  conditions  of 
borrowing  among  the  poor*  shows   that  the  chief  causes 

'  Ibid.,  p.  44.  '  Ibid.,  p.  35.  ^  Ibid  ,  pp.  40-42. 

♦U.S.  Bureau  of  Labor  Bulletin,  No.  64,  May,  1906,  pp.  622  flf. 


312  THE   RATE  OF  INTEREST  [Chap.  XV 

for  borrowing  are  a  death  or  birth  in  the  family,  or  pro- 
tracted ilhiess,  the  expense  of  which,  even  when  amount- 
ing to  only  $10  or  $20,  would,  without  the  loan,  make 
serious  inroads  on  the  daily  necessities. 

We  may  see  the  operation  of  the  same  principle  on  a 
larger  scale  in  the  case  of  the  San  Francisco  earthquake, 
which,  had  it  not  been  for  the  succor  rendered  by  the  whole 
country,  would  have  cut  down  the  income-stream  of  the 
city  to  the  starvation  point.  In  addition  to  the  aid  of  many 
millions  of  dollars  of  gifts,  there  were  needed  also  heavy 
loans.  AVliether  these  loans  were  used  to  produce  sus- 
tenance, which  is  direct  income,  or  to  offset  the  cost  of 
rebuilding  the  city,  which  is  outgo,  the  effect  is  the  same, 
—  they  were  for  the  purpose  of  salving  over  a  temporary 
injury  to  the  income-stream.  The  effect  on  the  rate  of 
interest  was  slight,  because  of  the  opportunity  to  borrow 
heavily  from  outside.  Had  the  city  not  had  this  opportu- 
nity, the  depression  in  its  income-stream  could  not  have  been 
mitigated,  and  the  rate  of  interest  would  inevitably  have 
risen  to  a  level  comparable  with  that  which  prevailed  in  the 
same  region  a  half  century  ago  during  the  gold  fever. 

In  much  the  same  way  is  the  income-stream  of  a  nation 
affected  by  war.  The  effects  in  this  case,  however,  are 
more  complex,  owing,  first,  to  the  element  of  uncertainty 
which  the  war  introduces  until  peace  is  declared;  and, 
secondly,  to  the  fact  that  wars  are  apt  to  be  more  pro- 
tracted than  most  other  misfortunes.  The  effect,  accord- 
ing to  previous  explanations,  should  be  that  at  the  beginning 
of  the  war  the  rates  of  interest  on  risky  loans  would  be  high. 
This  would  be  especially  true  of  the  loans  the  periods  of 
which  are  short,  or  not  long  enough  to  outlast  the  war.  On 
the  other  hand,  the  rate  of  interest  on  safe  loans  would  be 
lowered  for  short-term  loans,  and  raised  for  long-term  loans. 
A  short-term  loan  relates  to  a  descent  in  the  income  curve 
if  repayable  at  a  time  when  the  income-stream  is  apt  to  be 
still  further  reduced.  This  descent  in  the  income-stream, 
together  with  the  element  of  uncertainty,  tends,  as  has  been 


Sec.  12]      INDUCTIVE  VERIFICATION   (ECONOMIC)  313 

seen,  to  lower  the  rate  of  interest  on  safe  loans.  On  the 
other  hand,  for  long-term  loans  intended  to  outlast  the 
war,  the  rate  of  interest  is  apt  to  be  high,  for  the  income- 
stream  at  the  time  of  repayment  may  be  expected  to  exceed 
the  income-stream  at  the  time  of  contract. 

At  the  close  of  the  war,  after  peace  is  declared  and  the 
element  of  uncertainty  introduced  by  it  has  disappeared, 
the  rate  of  interest,  even  on  short-term  loans,  will  be  high  ; 
for  then  the  country  is,  as  it  were,  beginning  anew,  and 
the  same  causes  operate  to  make  interest  high  as  apply  in 
the  case  of  all  new  countries.  The  situation  at  this  period 
is  exemplified  by  the  recent  peace  loan  for  Japan. 

"V\Tien  the  effects  of  the  war  include  the  issue  of  depre- 
ciated paper  money,  the  rate  of  interest  is  affected  in  a 
somewhat  more  complex  manner,  being  then  subject 
to  the  influence  of  depreciation,  according  to  the  princi- 
ples explained  in  Chapter  V,  and  statistically  verified  in 
Chapter  XIV. 

Among  the  most  powerful  causes  which  affect  the  time- 
shape  of  income-streams  has  been  noted  the  effect  of  inven- 
tion. That  the  claims  which  have  been  made  for  the  effect 
of  invention  are  verified  in  fact  can  scarcely  be  doubted 
when  we  consider  the  history  of  railway  transportation. 
The  very  fact  that  during  the  last  half  century  the  chief 
outlet  for  investors'  savings  has  been  in  the  creation  of  new 
railways,  is  sufficient  testimony.  What  is  true  in  the  case 
of  this  single  invention  or  group  of  inventions  is  more  sig- 
nally true  when  a  large  number  of  inventions  is  being  made. 
The  effect  of  the  activity  of  the  inventive  faculty  must  have 
materially  contributed  to  keep  up  the  rate  of  interest  in 
the  United  States,  and  during  the  last  generation  in  Ger- 
many. 

The  striking  way  in  which  the  rate  of  interest  in  Germany 
has  been  maintained  during  the  past  century  is  shown  by  the 
experience  of  the  Gotha  Mutual  Life  Insurance  Company, 
the  largest  in  Germany.  From  1829  to  1838,  this  company 
made  an  average  rate  of  3.9  per  cent.     During  the  years 


314  THE  RATE   OF   INTEREST  [Chap.  XV 

1850-1852,  the  rate  realized  was  3.9  per  cent.  In  1874, 
the  rate  had  risen  to  4.8,  influenced  partly  by  the 
same  causes  that  had  affected  the  interest  rate  all  over 
the  world,  and  partly  by  the  great  industrial  progress 
which  Germany  was  making.  In  1885,  the  rate  had  fallen 
to  4,2  per  cent.,  and  in  1902  to  3.9  per  cent.,  a  rate  the 
same  as  that  which  had  been  realized  three  quarters  of  a 
century  before !  ^ 

§  13 

We  have  considered  the  effect  on  the  rate  of  preference 
of  those  changes  in  the  income-stream  due  to  the  growth 
or  waning  of  natural  resources  and  to  the  temporary  in- 
fluence of  misfortunes  and  inventions.  There  remain  to 
be  considered  those  regular  changes  in  the  income-stream 
of  a  rhythmic  or  seasonal  character.  Though  most  persons 
are  not  aware  of  the  fact,  it  can  scarcely  be  doubted  that 
the  annual  succession  of  seasons  produces  an  annual  cycle 
in  the  income-stream  of  the  community.  This  is  especially 
true  of  agriculture.  Grains,  fruits,  vegetables,  cotton, 
wool,  and  almost  all  the  organic  products  flow  from  the 
earth  at  an  uneven  rate,  and  require  for  their  production 
also  an  uneven  expenditure  of  labor  from  man  during  dif- 
ferent seasons  of  the  year.  Statistics  of  consumption  show 
that  the  income  enjoyed  conforms  in  general  to  a  cycle. 
Food  products  are  usually  made  available  in  the  warm 
months  when  crops  ripen ;  logs  are  hauled  out  of  the  woods 
in  winter,  floated  to  mills  in  spring,  and  made  into  lumber 
in  summer. 

But  the  tendency  to  a  cycle  is  modified  by  the  existence 
of  stocks  of  commodities  to  tide  over  the  periods  of  scarcity. 
The  ice  of  winter  is  stored  for  summer,  and  the  fruits  of 
summer  are  canned  and  preserved  for  winter.  Only  so 
far  as  such  storage  and  preservation  are  difficult  and  ex- 
pensive, or  impair  the  quality  of  the  goods  thus  held  over, 
or,  because  of  the  perishable  nature  of  the  goods,  are  im- 

*  See  Zartman,  The  Investments  of  Life  Insurance  Companies, 
pp.  105-106. 


Sec.  13]      INDUCTIVE  VERIFICATION  (ECONOMIC)  315 

practicable,  does  there  remain  any  cyclic  change  in  enjoyed 
income.  The  cycle  is  different  for  different  industries  and 
for  different  classes  of  the  population.  The  farmer  is 
perhaps  the  most  typical  for  the  country  as  a  whole.  For 
him  the  lowest  ebb  is  in  the  fall,  when  gathering  and  market- 
ing his  crops  cause  him  a  sudden  expenditure  of  labor,  or 
of  money  for  the  labor  of  others.  To  tide  him  over  this 
period  he  may  need  to  borrow.  A  whole  group  of  other 
industries,  particularly  those  cormected  with  transporta- 
tion, experience  a  sympathetic  fluctuation  in  the  income- 
stream.  In  the  parlance  of  Wall  Street,  "  money  is  needed 
to  move  the  crops."  The  rate  of  interest  tends  upward, 
as  the  following  table  shows : '  — 

MONTHLY   DISCOUNT    RATES    FOR    PRIME  TWO-NAME 

60   TO    90    DAYS'  PAPER    IN    NEW    YORK    CITY 

(Average  for  10  years,  1896-1905) 

January 4.3 

February 4.1 

March 4.4 

April 4.4 

May 4.1 

June 3.9 

July 4.2 

August 4.7 

September 5.2 

October 5.2 

November 4.8 

December 4.8 

In  a  community  dominated  by  some  other  industry  than 
farming  the  cycle  would  be  different.  Even  in  the  above 
table  the  rates  are  of  course  a  composite  in  which  the  cycles 
of  the  manufacturer  and  of  other  elements  are  superimposed 
upon  the  cycle  of  the  farmer.  The  manufacturer's  cycle 
is  a  little  later  than  the  farmer's  and  shifts  the  high  rates 
from  fall  toward  winter. 

Accordingly  in  England,  which  is  more  dominated  by  the 
manufacturer,  the  cycle,  though  similar  to  that  just  observed 

'  Compiled  from  daily  rates  given  in  The  Financial  Review. 


316  THE   RATE  OF  INTEREST  [Chap.  XV 

for  the  United  States,  is  shifted  forward,  as  the  following 
table  shows  :^  — 

MONTHLY  AVERAGES  OF  MINIMUM  RATE  OF  DISCOUNT 

OF   BANK   OF   ENGLAND   FOR  YEARS  1845-1900 

January        4.0 

February 3.6 

March 3.5 

April 3.4 

May 3.6 

June 3.4 

July 3.3 

August 3.4 

September 3.4 

October 3.9 

November 4.2 

December 4.1 

§  14 

The  facts  as  presented  in  this  chapter  harmonize  with 
the  theory  as  presented  in  previous  chapters.  Accord- 
ing to  the  theory,  if  there  is  a  high  degree  of  foresight, 
self-control,  and  regard  for  posterity,  or  if  income-streams 
are  large  or  plentiful  in  the  food-element,  or  have  a  descend- 
ing time-shape,  then,  other  things  being  equal,  the  rate  of 
interest  will  be  low,  or  capital  will  be  accumulated,  or  the 
community  will  lend  to  other  communities,  or  the  instru- 
ments it  creates  will  be  durable.  We  find  these  results 
present  in  actual  fact  where  the  antecedent  conditions 
enumerated  are  also  present.  Reversing  the  conditions, 
we  find  reversed  results.  Of  course  this  inductive  veri- 
fication is  very  rough,  since  we  never  can  assert  that 
"other  things  are  equal,"  and  thus  isolate  and  measure 
any  one  particular  factor,  as  in  the  more  exact  inductions 
of  physical  science.  Yet  the  inductive  study  is  worth 
something,  even  if  it  be  only  in  the  fact  that  it  does  not 
contradict  the  theory ;  for  a  false  theory  usually  encounters 
facts  with  which  it  cannot  be  reconciled. 

*  See  Palgrave's  Bank  Rate  and  the  Money  Market,  New  York  (Dut- 
ton),  1903,  p.  97. 


CHAPTER  XVI 

INDUCTIVE   REFUTATION   OF   " MONEY  THEORY" 

§    1 

It  would  be  impracticable,  even  if  it  were  worth  while, 
to  array  before  the  tribunal  of  facts  all  the  rival  theories 
of  interest  which  have  been  presented.  We  must  rest  our 
case  largely  on  the  statement  of  principles  which  has  already 
been  made.  It  was  shown,  for  instance,  that  the  common 
theory,  that  interest  varies  inversely  with  the  quantity 
of  money,  was  superficial,  since  money  is  merely  a 
means  for  obtaining  capital.  It  was  also  shown  that  the 
theories  commonly  given  in  economic  text-books,  that  the 
rate  of  interest  depends  on  ''quantity  of  capital,"  are  only 
a  little  less  superficial,  since  capital  itself  is  merely  a  means 
to  income.  We  cannot  reach  the  ultimate  regulator  of 
interest  until  we  reach  income ;  and  it  is  only  because  of 
the  lack  of  an  adequate  theory  of  income  that  economists 
have  been  content  with  analyses  so  incomplete. 

It  is  often  true  that  up  to  a  certain  point  facts  may  be 
adduced  even  in  support  of  a  false  theory.  It  could  doubt- 
less be  shown,  for  instance,  that  interest  was  often  high 
when  capital  was  scarce,  and  vice  versa.  The  crucial  test, 
however,  comes  when  an  income-stream  of  an  ascending 
type  occurs  where  capital  is  plentiful,  or  of  a  descending 
type  where  capital  is  scarce.  If  incomes  are  rising,  though 
capital  be  plentiful,  interest  will  be  high,  as  in  the  United 
States  recently;  and  if  incomes  are  falling,  though  capital 
be  scarce,  interest  will  be  low.  As  soon  as  economists  think 
in  terms  of  income,  and  give  up  thinking  in  terms  of  capital, 
which  is  merely  an  expression  for  contemplated  income, 
there  can  be  no  difficulty  in  reaching  a  correct  view  of  the 
problem,  without  the  necessity  of  confuting  all  previous 

theories  by  special  facts. 

317 


318  THE   RATE   OF  INTEREST  [Chap.  XVI 

The  only  theory  for  which  its  adherents  will  demand  a 
test  by  facts  is  the  theory,  believed  by  many  business  men, 
that  the  rate  of  interest  varies  inversely  with  the  quantity 
of  money.  This  theory,  in  spite  of  having  been  refuted 
by  economists  for  over  a  hundred  years,  is  still  dominant 
among  many  if  not  most  business  men.  The  business  man 
prides  himself  on  reasoning  by  facts,  and  it  is  only  by  mis- 
reading facts,  and  not  by  any  analysis  of  the  problem,  that 
he  inclines  to  the  money-theory  of  interest.  It  follows 
that  only  by  facts  can  he  be  convinced  of  his  error.  As 
Moody's  Magazine  well  says :  ^  — 

"Slowly  but  surely  the  great  financial,  commercial,  and  business 
men  of  the  world  are  reaching  the  conclusion  .  .  .  that  an  increased 
supply  of  gold  means  higher,  rather  than  lower,  interest  rates. 
Most  converts,  however,  are  converts  from  the  force  of  facts,  rather 
than  from  reason  and  logic." 

§  2 

So  far  as  the  matter  of  appreciation  in  its  relation  to  in- 
terest goes,  facts  have  already  been  adduced  in  sufficient 
numbers  in  Chapter  XIV.  At  present  we  are  to  consider 
the  theory  that  high  rates  of  interest  are  associated  with 
scarce  money,  and  low  rates  with  plentiful  money.  Since 
in  general  it  is  true  that  plentiful  money  means  high  prices, 
and  scarce  money  low  prices,  if  this  theory  were  correct, 
we  should  expect  to  find  that  during  those  years  when  prices 
were  high,  rates  of  interest  would  be  low,  and  vice  versa. 

In  the  following  table  we  see  that  there  is  no  such  inverse 
correlation  between  prices  and  interest  as  this  theory  calls 
for.  Tlie  columns  of  the  table  relate  respectively  to  dif- 
ferent decades.  Two  rates  of  interest  are  given  for  each 
decade.  The  first,  written  opposite  "high  prices,"  is  the 
average  rate  for  those  years  of  the  decade  whose  price-levels, 
as  shown  by  an  index-number,  were  above  the  average  price- 
level  for  the  whole  decade;  the  second  is  the  average  rate 
for  the  years  whose  prices  were  below  the  general  average : — 

1  August,  1906. 


Sec.  2]    REFUTATION  OF  "MONEY  THEORY" 


319 


MARKET  RATES  OF  INTEREST  IN  RELATION  TO   HIGH 

AND    LOW    PRICES' 


1824 

to 
1831 
incl. 

3.8 
3.2 

1832 

to 
1841 
incl. 

1842 

to 
1851 
incl. 

1852 

to 
1861 
incl. 

1862 

to 
1871 
incl. 

1872 

to 
1881 
incl. 

1882 

to 
1891 
incl. 

London,      High  prices  . 
London,      Low  prices  . 

4.4 
3.2 

3.6 

2.6 

5.4 
3.0 

9.1 
9.1 

5.1 
2.6 

7.4 
6.7 

3.7 
2.5 

3.0 
2.5 

New  York,  High  prices  . 
New  York,  Low  prices  . 

7.0 
5.1 

5.3 
5.1 

Berlin,        High  prices  . 
Berlin,        Low  prices   . 

4.6 
3.4 

3.7 
3.2 

3.3 
2.7 

Paris,          High  prices  . 
Paris,          Low  prices  . 

• 

4.1 
2.4 

2.6 

2.6 

^  Calcutta,    High  prices  . 
Calcutta,    Low  prices   . 

6.2 
5.6 

5.4 
6.2 

^  Tokyo,        High  prices  . 
Tokyo,        Low  prices  . 

12.3 
12.0 

10.1 
10.1 

*  Shanghai,  High  prices  . 
Shanghai,  Low  prices   . 

• 

6.0 

5.7 

Of  the  21  comparisons  contained  in  this  table, 
17  show  higher  rates  for  high-price  years  than  for  low-price 

*  This  table  is  constructed  from  the  data  given  in  the  Appendix 
to  Ch.  XIV.  For  New  York,  the  rates  for  the  first  decade  are  aver- 
aged from  the  column  in  the  Appendix  headed  "60  days,"  and  are 
not  to  be  compared  with  those  for  the  remaining  decades,  which  are 
averaged  from  the  column  headed  "Prime  two-name  60  days."  The 
index-numbers  of  prices  which  have  been  employed  are  those  of 
Jevons  (1824-1851),  and  Sauerbeck  (1852-1891)  for  England,  Soet- 
beer  and  Heinz  for  Germany,  the  Aldrich  Senate  report  for  the  United 
States  and  France,  and  the  Japanese  report  for  India,  Japan,  and 
China.     (See  Appendix  to  Ch.  XIV,  §  3.) 

^  For  Calcutta  the  rate  for  the  bank  of  Bengal  is  employed,  no 
"market"  rate  being  available.  The  first  column  is  for  1873-1881 
instead  of  1872-1881,  for  the  reason  that  no  index-number  for  1872 
is  available. 

'  For  Tokyo  the  first  column  is  for  1873-1881  for  the  same  reason. 

*  For  Shanghai  the  period  is  1885-1893  in.stead  of  1882-1891, 
for  the  reason  that  the  available  rates  begin  in  1885  and  the  index- 
numbers  end  in  1893. 


320  THE  RATE  OF   INTEREST  [Chap.  XVI 

years,  one  shows  the  opposite  condition,  and  3  show 
equal  rates  in  the  two  cases.  As  the  table  covers  68  years 
for  London,  40  for  New  York,  30  for  Berlin,  20  for  Paris, 
19  each  for  Calcutta  and  Tokyo,  and  9  for  Shanghai,  or 
205  years  in  the  aggregate,  the  result  may  be  accepted  with 
great  confidence  that  high  and  low  prices  are  usually  as- 
sociated with  high  and  low  interest  respectively. 

There  are  two  probable  reasons  for  this  connection.  One 
is  that  a  high  price-level  is  often  due  to  a  temporary  scarc- 
ity of  enjoyable  commodities,  as  in  a  beleaguered  city,  in 
San  Francisco  after  the  earthquake  and  fire  when  bread  was 
a  dollar  a  loaf,  or  in  the  Klondike  during  the  gold  fever. 
In  such  cases  the  rate  of  interest  is  high  for  economic, 
not  monetary,  reasons,  — because,  in  fact,  of  the  relative 
scarcity  of  present  real  income. 

The  second  reason  is  that  the  years  of  high  prices  are 
usually  the  culminations  of  periods  of  rising  prices,  during 
which  the  rate  of  interest  has  been  rising  through  the  de- 
preciation of  money,  in  accordance  with  the  principles  ex- 
plained in  Chapters  V  and  XIV.  If  the  tables  given  in  the 
Appendix  are  examined,  it  will  be  found  that  prices  usually 
rise  to  a  point,  and  then  often  break  suddenly  after  a  crisis. 
The  high-price  years  in  this  case  evidently  belong  more  often 
to  the  period  of  rising  than  to  the  period  of  falling  prices. 

§  3 

Wliatever  be  the  correct  explanation,  the  facts  give  no 
countenance  to  the  theory  that  the  rate  of  interest  depends 
upon  the  supply  of  money. 

It  may  be  said  that  the  preceding  table  is  not  conclusive, 
owing  to  the  fact  that  the  correlation  it  shows  is  one  of 
prices  and  interest,  and  not  directly  of  quantity  of  money 
and  interest.  But  this  objection  can  be  readily  met  by 
constructing  another  table  in  which  per  capita  circulation 
of  money  is  stated  in  conjunction  with  the  rates  of 
interest :  — 


Sec.  3]         REFUTATION  OF  "MONEY  THEORY" 


321 


RATES   OF  INTEREST  IN  RELATION  TO   PER    CAPITA 

CIRCULATION 


Per  Capita  Money 

Interest  Rate  in  N.  Y. 

IN  Circulation 

(Prime  Two-Name 

IN  U.S.  July  1 

60  Days) 

1871 

18.10 

6.1 

1872 

18.19 

8.0 

1873 

18.04 

10.3 

1874 

18.13 

6.0 

1875 

17.16 

5.5 

1876 

16.12 

5.2 

1877 

15.58 

5.2 

1878 

15.32 

4.8 

1879 

16.75 

5.0 

1880 

19.41 

5.2 

1881 

21.71 

5.2 

1882 

22.37 

5.7 

1883 

22.91 

5.5 

1884 

22.65 

5.2 

1885 

23.02 

4.1 

1886 

21.82 

4.7 

1887 

22.45 

5.7 

1888 

22.88 

4.9 

1889 

22.52 

4.8 

1890 

22.82 

6.0 

1891 

23.42 

5.7 

1892 

'          24.56 

4.3 

1893 

24.03 

7.1 

1894 

24.52 

3.4 

1895 

23.20 

3.8 

1896 

21.41 

5.8 

1897 

22.87 

3.4 

1898 

25.15 

3.8 

1899 

25.58 

4.2 

1900 

26.94 

4.4 

1901 

27.98 

4.4 

1902 

28.43 

4.9 

1903 

29.42 

5.5 

1904 

30.77 

4.2 

1905 

31.08 

4.3 

322  THE  RATE  OF   INTEREST  [Chap.  XVI 

An  examination  of  this  table  will  show  that  the  per  capita 
circulation  goes  up  and  down  quite  independently  of  the 
fluctuations  of  the  rate  of  interest.  If  the  money  theory 
were  true  we  should  expect  that  when  money  shrank,  in- 
terest would  rise,  and  reversely.  The  two  should  vary  in- 
versely. But  as  a  matter  of  fact,  out  of  the  thirty-four 
pairs  of  consecutive  years,  we  find  that  interest  varied  about 
as  often  directly  as  it  did  inversely  with  the  per  capita  cir- 
culation. To  be  exact,  it  varied  inversely  in  15^  and 
directly  in  18|  cases.^  Thus  it  happened  to  move  a  little 
oftener  in  the  manner  opposed  to  the  money  theory  than 
in  the  manner  favorable  to  that  theory. 

A  statistical  study  of  the  rates  of  interest  and  the  pro- 
duction of  the  precious  metals  made  by  B.  R.  G.  Levy  leads 
to  the  same  conclusion,  that  the  rate  of  interest  is  not  related 
to  the  quantity  of  money.^ 

§  4 

The  preceding  facts  must  convince  any  one  open  to  con- 
viction that  the  rate  of  interest  is  not  inversely  correlated 
to  the  quantity  of  money.  But  business  men  familiar 
with  banking  will  not  be  satisfied  until  some  place  is  found 
in  our  theory  of  interest  for  the  common  observation  that 
if  money  in  general  does  not,  certainly  bank  reserves  do 
vary  inversely  with  the  rate  of  interest.  That  this  ob- 
servation is  correct  is  not  questioned.  It  is  the  established 
policy  of  large  banks,  like  the  Bank  of  England,  to  protect 
their  reserve  by  raising  the  rate  of  interest.  From  these 
facts  the  conclusion  is  drawn  that  the  scarcity  of  bank 
reserves  produces  a  high  rate  of  interest.  But  the  facts 
fit  in  with  the  present  theory  of  interest  quite  as  well  as 

*  When  the  rate  remained  the  same  in  two  consecutive  years, 
it  was  counted  as  one  half  a  variation  both  ways. 

*  "Du  taux  actuel  de  I'int^rSt  et  de  scs  rapports  avec  la  production 
des  m6taux  pr^cieux  et  les  autres  ph6nom(^nes  economique."  B.  R. 
G.  Levy,  Journal  des  Economistes,  March,  1899,  p.  334;  April,  1899, 
p.  28. 


Sec.  4]        REFUTATION  OF  "MONEY  THEORY"  323 

with  the  fallacious  money  theory  of  interest.  A  low  bank 
reserve  is  merely  a  symptom  of  a  general  ebb  tide  in  the 
income  of  the  community.  A  bank  of  discount  and  deposit 
stands  between  those  who  have  surplus  income  to  deposit 
and  those  who  wish  to  eke  out  a  lean  income  by  borrowing. 
Those  persons  whose  income  is  larger  than  they  need  to-day 
are  the  ones  who  swell  the  deposits  of  a  bank.  When  a 
farmer  receives  for  his  crops  more  money  than  he  cares 
at  once  to  turn  into  enjoyable  income,  he  deposits  some  of 
it  in  a  bank  or  trust  company — with  interest  if  possible, 
without  it  if  necessary.  On  the  other  hand,  the  same 
farmer,  before  his  crop  is  sold,  may  wish  to  discount  a  note 
at  the  bank  in  order  to  pay  off  his  help.  Bank  deposits 
grow,  as  compared  with  loans,  when  men's  incomes  are 
temporarily  flush,  that  is,  when  their  income-curves  are 
descending;  loans  grow  as  compared  with  deposits  when 
their  incomes  are  temporarily  scant,  that  is,  when  their 
income-curves  are  ascending.  The  banker  must  keep  in 
equilibrium  between  the  two  classes  of  customers,  those 
who  discount  and  those  who  deposit.  If  the  loans  increase 
too  much,  the  banker's  reserve  will  be  endangered ;  if  the 
deposits  accumulate,  it  will  be  idle.  He  regulates  his 
reserve  by  adjusting  the  rate  of  discount,  raising  it  if  his 
reserve  is  low,  or  lowering  it  if  it  is  high.  To  him,  his  action 
appears  in  the  light  of  protecting  and  utilizing  his  reserve ; 
but  the  banker  is  not  the  prime  factor.  Back  of  the 
reserve  are  the  real  causes,  — the  state  of  the  incomes  of 
his  customers.  If  ascending  incomes  are  predominant, 
the  reserve  will  need  more  "protection"  than  in  the  con- 
trary case.  A  rise  of  the  discount  rate  is  therefore  due, 
in  the  last  analysis,  to  the  predominance  of  ascending 
incomes,  and  a  fall,  to  the  predominance  of  incomes  of  the 
opposite  type.  The  reserve  is  merely  the  football  between 
the  two  sets  of  persons,  those  who  deposit  and  those  who 
loan.  The  business  man  regards  the  rate  of  interest  too 
much  from  the  banker's  point  of  view.  A  banker  or  broker 
is  merely  an  intermediary.     To  regard  him,  or  the  gold  that 


324  THE  RATE  OF  INTEREST  [Chap.  XVI 

happens  to  be  in  his  vaults,  as  primary  influences  on  the 
rate  of  interest  is  as  erroneous  as  to  regard  the  operations 
of  a  grain  broker  as  primary  influences  upon  the  price  of 
wheat,  or  those  of  a  real  estate  agent  as  primary  influences 
upon  the  price  of  land.  The  banker  enables  the  lenders 
and  borrowers  to  find  each  other ;  they,  and  not  he,  in  the 
end  fix  the  rate  of  interest/ 

The  theory  of  interest  which  does  not  look  beyond  the  bank 
coffers  is  almost  as  crude  as  the  theory  which  would  ascribe 
the  weather  to  the  thermometer.  In  a  Western  town  a 
servant  was  being  instructed  to  prepare  a  bath  at  a  partic- 
ular temperature,  and  was  shown  the  point  recorded  by  the 
thermometer  when  the  bath  was  at  the  right  temperature. 
To  the  consternation  of  the  housekeeper,  when  the  servant 
had  prepared  the  bath  the  next  day  its  temperature  was 
found  to  be  far  too  cold.  The  servant  explained  that  she 
had  used  the  "conjure  stick," referring  to  the  thermometer, 
but  that  it  didn't  seem  to  heat  the  water  at  all !  Many 
persons  have  a  similar  superstition  that  money  is  a  sort  of 
"conjure  stick"  potent  to  regulate  the  rate  of  interest, 
whereas  in  fact  it  is  only  a  thermometer  to  faithfully  record 
the  variations  of  that  rate.  When  there  is  "  plenty  of  money 
in  Wall  Street,"  interest  is  low,  and  vice  versa;  but  the  causes 
which  have  influenced  interest  are  the  causes  which  have 
put  the  money  on  loan  in  Wall  Street. 

§  5 

The  money-theory  comes  nearest  to  scoring  a  point  when 
applied  to  panics,  for  during  a  time  of  panic  it  is  true  that 
money  loans  are  sought  to  be  used  as  solvents  of  debts. 
This  fact  has  often  puzzled  economists  who,  while  dis- 
believing the  money-theory  of  interest  in  general,  have 
felt  that  in  this  case  at  least  it  was  true.^    It  is  clear,  how- 

'  Cf .  George  Clare,  "  A  Money  Market  Primer,"  London  (Effingham 
WUson),  1905,  pp.  134-135. 

^  See  Mill,  Principles  of  Political  Economy,  Book  3,  Chap.  XXIII, 

J  4. 


Sec.  5]        REFUTATION  OF  "  MONEY  THEORY "  325 

ever,  that  even  a  panic  loan,  from  Peter  to  pay  Paul,  is  a 
case  of  an  effort  to  maintain  the  even  flow  of  one's  income- 
stream.  The  alternative,  if  one  does  not  borrow,  is  to  sell 
some  of  one's  goods,  necessitating  the  sacrifice  of  the  income 
which  they  are  designed  to  bring.  The  choice  between  the 
loan  and  the  sale  is  between  the  necessity  of  repaying  the 
loan  when  due,  and  the  necessity  of  losing  the  income  from 
the  goods,  —  a  choice  between  two  bits  of  income  different 
in  amount,  or  kind,  or  distribution  in  time.  The  loan  sub- 
stitutes one  of  these  bits  of  income  for  the  other,  and  is 
therefore  in  this  respect  exactly  similar  to  any  other  loan. 
If  one's  solvency  is  in  question,  the  same  exchange  occurs 
in  a  somewhat  different  form ;  the  loan  is  then  undertaken 
in  preference  to  the  deformation  of  the  income-stream 
which  insolvency  involves. 

It  is  true,  however,  that  money,  as  money,  is  more 
vitally  related  to  panic  loans  than  to  any  other.  In  or- 
dinary loans,  money  enters  merely  as  a  convenient  medium 
for  securing  something  else  —  capital,  and  through  that 
capital,  income ;  in  a  panic  loan,  however,  the  money  enters 
as  a  necessary  medium  for  the  legal  discharge  of  a  debt. 
Again,  in  an  ordinary  loan,  the  borrower  is  free  to  adjust 
the  amount  borrowed  according  to  the  rate  of  interest ; 
in  a  panic  loan,  on  the  other  hand,  there  is  no  such  elastic 
choice.  The  borrower  must  borrow  that  fixed  amount 
necessary  to  discharge  his  debt,  even  if  the  rate  of  interest 
is  exorbitant.  If  physical  money  is  not  sufficient  to  allow 
debtors  to  discharge  their  debts,  the  rate  of  interest  will 
be  high  and  there  can  be  no  escape  from  it  as  in  ordinary 
times.  In  this  case  it  may  be  truly  said  that  scarcity  of 
money  has  made  interest  high.  Money  of  any  kind  brought 
into  the  market  will  relieve  the  stringency  and  lower  the 
rate  of  interest.  The  United  States  has  accomplished  this 
by  prepaying  interest  on  bonds,  and  the  clearing  house  has 
accomplished  it  by  issuing  clearing-house  certificates.  It 
is  therefore  important,  in  order  not  to  have  violent  changes 
in  the  rate  of  interest,  that  the  currency  should  be  elastic. 


326  THE  RATE  OF  INTEREST  [Chap.  XVI 

A  panic  is  always  the  result  of  unforeseen  conditions ;  and 
among  those  unforeseen  conditions,  and  partly  as  a  con- 
sequence of  other  unforeseen  conditions,  is  scarcity  of  money 
on  loan.  Under  ordinary  and  normal  conditions,  money  on 
loan  is  so  automatically  adjusted  as  to  make  it  a  mere  trans- 
mitter through  the  medium  of  which  borrowers  and  lenders 
act  upon  the  rate  of  interest,  just  as  a  smooth-running  gear 
transmits  power  from  one  wheel  to  another,  without  ex- 
erting any  independent  force  itself.  But  when  the  gear  gets 
out  of  order  it  may  stick  and  offer  a  resistance  of  its  own 
to  the  wheels  with  which  it  is  in  contact. 

It  is  therefore  not  asserted  that  money  plays  no  role  in 
determining  the  rate  of  interest.  But  its  role  is  a  minor 
one,  and  very  different  from  that  often  assigned  to  it. 
Its  role  normally  is  to  efface  itself  and  merely  facilitate 
the  frictionless  working  of  economic  machinery.  Under 
the  abnormal  conditions  of  a  panic,  the  dearth  of  it 
may  create  friction  and  enhance  interest  at  that  particular 
point. 

Finally,  as  we  have  seen  in  previous  chapters,  a  change 
in  the  monetary  standard  will  affect  the  number  by  which 
the  rate  of  interest  is  expressed,  increasing  it  if  the  monetary 
standard  is  depreciating,  and  decreasing  it  if  the  standard 
is  appreciating. 

With  these  reservations,  we  may  say  that  the  rate  of 
interest  is  not  affected  by  the  quantity  of  money. 


CHAPTER  XVII 

SUMMARY 
§    1 

We  have  seen  that  the  rate  of  interest  is  subject  to  both 
a  nominal  and  a  real  variation,  the  nominal  variation  being 
that  connected  with  changes  in  the  standard  of  value,  and 
the  real  variation  being  that  connected  with  the  other  and 
deeper  economic  causes.  As  to  the  nominal  variation  in 
the  rate  of  interest,  we  found  that,  theoretically,  an  ap- 
preciation of  1  per  cent,  of  the  standard  of  value  in  which 
the  rate  of  interest  is  expressed,  compared  with  some  other 
standard,  will  reduce  the  rate  of  interest  in  the  former 
standard,  compared  with  the  latter,  by  about  1  per  cent. ; 
and  that,  contrariwise,  a  depreciation  of  1  per  cent,  will 
raise  the  rate  by  that  amount.  Such  a  change  in  the  rate 
of  interest,  however,  is  merely  a  change  in  the  number 
expressing  it,  and  not  in  any  sense  a  real  change.  Yet 
the  appreciation  or  depreciation  of  the  monetary  standard 
does  produce  a  real  effect  on  the  rate  of  interest,  and  that 
a  most  vicious  one.  This  effect  is  due  to  the  fact  that  the 
rate  of  interest  does  not  change  enough  to  fully  compensate 
for  the  appreciation  or  depreciation.  Thus,  if  the  monetary 
standard  is  appreciating  at  the  rate  of  3  per  cent,  per  annum 
and  the  rate  of  interest  falls  only  2  per  cent.,  the  deficiency 
of  1  per  cent,  shows  that  the  rate  of  interest  has  not  really 
fallen,  but  risen.  This  rise  of  1  per  cent,  is  abnormal, 
being  the  result  of  an  error  in  prediction.  Had  the  debtors 
and  creditors  concerned  foreseen  fully  the  change  in  the 
monetary  standard,  they  would  have  forestalled  it  fully. 
Their  failure  so  to  do  results  in  an  unexpected  loss  to  the 
debtor,  and  an  unexpected  gain  to  the  creditor.     Wliat 

327 


328  THE  RATE  OF  INTEREST  [Chap.  XVII 

usually  happens,  therefore,  as  a  consequence  of  an  appre- 
ciation in  the  monetary  standard,  is  that  the  rate  of  interest 
nominally  falls,  but  really  rises,  whereas  in  the  contrary 
case,  if  the  monetary  standard  is  depreciating,  the  rate 
of  interest  nominally  rises,  but  really  falls.  It  is  conse- 
quently of  the  utmost  importance,  in  interpreting  the  rate 
of  interest  statistically,  to  ascertain  in  each  case  in  which 
direction  the  monetary  standard  is  moving,  and  to  re- 
member that  the  direction  in  which  the  rate  apparently 
moves  is  apt  to  be  precisely  the  opposite  of  that  in  which 
it  really  moves. 

§  2 

Turning  from  the  nominal  to  the  real  variation  in  the  rate 
of  interest,  we  see  that  the  rate  of  interest,  considered  in- 
dependently of  fluctuations  in  the  monetary  standard,  is 
determined  by  six  causes,  namely :  (1)  The  extent  of  the 
effective  range  of  choice  of  different  incomes  which  are 
open  to  each  individual ;  (2)  the  dependence  of  "  time-pref- 
erence" upon  prospective  income — its  size,  shape,  com- 
position, and  probability;  (3)  the  tendency  of  the  rates 
of  time-preference  for  different  individuals  to  become  equal 
to  each  other  and  to  the  rate  of  interest,  through  the  loan 
market,  or  through  buying  and  selling  property;  (4)  the 
tendency  of  the  various  "rates  of  return  on  sacrifice  "to  be- 
come equal  to  each  other  and  to  the  rate  of  interest,  through 
the  operation  of  free  choice  among  available  options ;  (5) 
the  fact  that  supply  and  demand  are  equal,  that  the 
modifications  in  the  income-streams  of  individuals  through 
buying  and  selhng  or  borrowing  and  lending  mutually 
offset  each  other  for  each  interval  of  time  considered,  — 
that  what  is  lent  must  equal  what  is  borrowed,  and  what 
is  gained  by  one  in  each  year's  income,  by  buying  and  sell- 
ing, is  lost  by  some  one  else;  (6)  the  fact  that,  for  the 
same  individual,  the  estimated  present  values  of  the 
changes  he  elects  to  make  in  his  prospective  income-stream 


Sec.  3]  SUMMARY  329 

mutually  offset  each  other;  that  is,  the  estimated  present 
value  of  what  he  borrows  is  equal  to  the  estimated  present 
value  of  what  he  returns,  or,  more  generally,  the  estimated 
present  value  of  an  addition  to  his  immediate  income  is 
equal  to  the  present  value  of  the  consequent  reduction  in 
his  future  income. 

Of  these  six  conditions,  many  are  so  inflexible  that  they 
have  little  influence  on  any  variation  in  the  rate  of  interest. 
The  last  four  are  of  this  relatively  fixed  type.  We  have 
remaining  the  first  two  as  the  only  causes  subject  to  im- 
portant variations.  The  fluctuations  in  these  causes  explain 
for  the  most  part  the  changes  in  the  rate  of  interest,  as 
actually  experienced.  We  shall  now  concentrate  attention 
upon  these  two,  —  the  range  of  known  choice  and  the  law 
of  time-preference. 

§  3 

As  to  the  range  of  choice,  each  individual  may,  as  assumed 
in  our  ''first  approximation,"  be  possessed  of  one  given  in- 
come which  is  rigid  (except  as  it  may  be  altered  by  borrow- 
ing and  lending) ;  or,  as  assumed  in  the  other  approxima- 
tions and  as  foimd  in  actual  fact,  he  may  be  possessed  of  a 
given  range  of  choice  of  many  different  income-streams. 
The  range  of  choice  actually  open  to  any  individual  will 
depend  principally  upon  the  amount  and  character  of  the 
capital-property  which  he  possesses.  It  follows  that, 
for  society  as  a  whole,  the  range  of  choice  of  incomes  will 
depend  upon,  first,  the  existing  capital  of  the  country ;  that 
is,  its  "resources,"  or  the  amount  and  character  of  the 
different  capital-instruments  existing  within  it  at  the  in- 
stant of  time  considered;  and,  secondly,  the  distribution 
of  ownership  of  these  capital-instruments  throughout  the 
community.  In  this  statement  it  is  intended,  of  course, 
to  include  under  capital-instruments  the  individuals  them- 
selves who  constitute  the  community,  for  they  are  the 
source,  through  their  personal  exertions,  of  much  of  the 


330  THE  RATE  OF  INTEREST  [Chap.  XVII 

income  which  they  enjoy.  In  short,  then,  the  available 
range  of  choice  will  depend  upon  capital  and  its  distribution. 
If  the  capital-instruments  of  the  community  are  of  such 
a  nature  as  to  offer  a  idde  range  of  choice,  we  have  seen  that 
the  rate  of  interest  will  tend  to  be  steady.  If  the  range  of 
choice  is  narrow,  the  rate  of  interest  will  be  comparatively 
variable.  If  the  range  of  choice  is  relatively  rich  in  the 
remotely  future  income  as  compared  with  the  more  immediate 
income,  the  rate  of  interest  will  be  high.  If  the  range  of 
choice  tends  to  favor  immediate  income  as  compared  with 
remote  future  income,  the  rate  of  interest  will  be  low. 
Thus,  for  the  United  States  during  the  last  century,  its 
resources  were  of  such  a  character  as  to  favor  a  remote 
future  income.  This  is  true,  for  a  time  at  least,  in  every 
undeveloped  country,  and,  as  we  have  seen,  gives  the  chief 
explanation  of  the  fact  that  the  rate  of  interest  in  such 
localities  is  usually  high. 

The  range  of  choice  in  any  community  is  subject  to  many 
changes  as  time  goes  on,  due  chiefly  to  one  of  three  causes. 
First,  a  progressive  increase  or  decrease  in  resources; 
second,  the  discovery  of  new  resources  or  means  of  develop- 
ing old  ones;  and  third,  change  in  political  conditions. 
The  impending  exhaustion  of  the  coal  supply  in  England 
which  has  been  noted  by  Jevons  and  other  writers  will  tend 
to  make  the  income-stream  from  that  island  decrease,  at  least 
in  the  remote  future,  and  this  in  turn  will  tend  to  keep  the 
rate  of  interest  there  low.  The  constant  stream  of  new 
inventions,  on  the  other  hand,  by  making  the  available 
income-streams  rich  in  the  remote  future,  tends  to  make 
the  rate  of  interest  high.  This  effect,  however,  is  confined 
to  the  period  of  exploitation  of  the  new  invention,  and  is  suc- 
ceeded later  by  an  opposite  tendency.  During  the  last  half 
century  the  exploitation  of  Stephenson's  invention  of  the 
locomotive,  by  presenting  the  possibility  of  a  relatively  large 
future  income  at  the  cost  of  comparatively  little  sacrifice 
in  the  present,  has  tended  to  keep  the  rate  of  interest  high. 
As  the  period  of  railroad  building  is  drawing  to  a  close,  this 


Sec.  4]  SUMMARY  331 

effect  is  becoming  exhausted,  and  the  tendency  of  the  rate 
of  interest,  so  far  as  this  influence  is  concerned,  is  to  fall. 
As  to  the  political  conditions  which  affect  the  rate  of  interest, 
insecurity  of  property  rights  such  as  occurs  during  politi- 
cal upheaval  tends  to  make  the  pure  or  "riskless"  rate  of 
interest  low.  At  the  same  time  it  adds  an  element  of  risk 
to  most  loans,  thereby  diminishing  the  number  of  safe  and 
increasing  the  number  of  unsafe  loans.  Hence  the  "com- 
mercial "  rate  of  interest  in  ordinary  loans  during  periods 
of  lawlessness  is  apt  to  be  high.  Reversely,  during  times 
of  peace  and  security,  the  "  riskless  "  rate  of  interest  is 
comparatively  high  while  the  "  commercial  "  rate  tends  to 
be  low. 

§  4 

We  turn  now  to  the  second  factor  determining  interest ; 
namely,  the  dependence  of  time-preference  of  each  in- 
dividual on  his  selected  income-stream.  We  have  seen 
that  the  rate  of  preference  for  immediate  as  compared  with 
remote  income  will  depend  upon  the  character  of  the  in- 
come-stream selected;  but  the  manner  of  this  dependence 
is  subject  to  great  variation  and  change.  The  manner  in 
which  a  spendthrift  will  react  to  an  income-stream  is  very 
different  from  the  manner  in  which  the  shrewd  accumulator 
of  capital  will  react  to  the  same  income-stream.  We  have 
seen  that  the  manner  in  which  the  time-preference  of  an 
individual  depends  upon  his  income  will  vary  with  five 
different  factors:  (1)  His  foresight  and  self-control;  (2) 
his  love  of  offspring  or  regard  for  posterity;  (3)  the  pro- 
spective length  and  certainty  of  his  life;  (4)  habit;  (5) 
fashion.  It  is  evident  that  each  of  these  circumstances 
may  change.  The  causes  most  likely  to  effect  such  changes 
are,  first,  education  and  training  in  thrift,  whether  accom- 
plished through  the  home,  the  school,  charitable  organi- 
zations, or  banks  for  small  savings,  building  and  loan  as- 
sociations, and  other  similar  institutions  calculated  to  have 
an  educational  influence;    second,  the  tendency  toward  or 


332  THE   RATE   OF   INTEREST  [Chap.  XVII 

away  from  a  spirit  of  extravagance  and  ostentation 
through  social  rivaby ;  ^  third,  the  changes  in  the  char- 
acter of  the  institutions  of  marriage  and  the  family  which, 
in  one  direction  or  the  other,  will  profoundly  affect  the 
love  of  offspring  and  regard  for  the  welfare  of  posterity; 
fourth,  the  development  of  the  science  of  hygiene  which  may 
tend  to  make  human  life  longer  and  more  certain;  fifth, 
the  causes  which  tend  to  make  the  distribution  of  wealth 
either  more  concentrated  or  diffused,  and  also  those  which 
tend  to  make  the  existing  economic  stratification  of  classes 
fixed  and  stereotyped  or  elastic  and  variable.  These  vari- 
ous factors  will  act  and  react  upon  each  other,  and  will 
affect  profoundly  the  rate  of  preference  for  present  over 
future  income,  and  thereby  influence  greatly  the  rate  of 
interest.  Where,  as  in  Scotland,  there  are  educational 
tendencies  which  instill  the  habit  of  thrift  from  childhood, 
the  rate  of  interest  tends  to  be  low.  Where,  as  in  ancient 
Rome,  there  is  a  tendency  toward  reckless  luxury  and  com- 
petition in  ostentation,  and  a  degeneration  in  the  bonds  of 
family  life,  there  is  a  consequent  absence  of  any  desire  to  pro- 
long income  beyond  one's  own  term  of  life,  and  the  rate  of 
interest  tends  to  be  high.  Where,  as  in  Russia,  wealth  tends 
to  be  concentrated  and  social  stratification  to  be  rigid,  the 
great  majority  of  the  community  on  the  one  hand,  through 
poverty  and  the  recklessness  which  poverty  begets,  tends  to 
have  a  high  rate  of  preference  for  present  over  future  income ; 
whereas,  at  the  opposite  end  of  the  ladder,  the  inherited 
habit  of  luxurious  living  tends,  though  in  a  different  way, 
in  the  same  direction.  In  such  a  community  the  rate  of 
interest  is  apt  to  be  unduly  high. 

§  5 

From  the  foregoing  enumeration,  it  is  clear  that  the  rate 
of  interest  is  dependent  upon  very  unstable  influences, 

*  See  Rae,  The  Sociological  Theory  of  Capital.  Cf .  the  writer's  "  Why 
has  the  Doctrine  of  Laissez  Faire  been  Abandoned?"  Science,  Jan.  4, 
1907. 


Sec.  5]  SUMMARY  333 

many  of  which  have  their  origin  deep  down  in  the  social 
fabric  and  involve  considerations  not  strictly  economic. 
Any  causes  tending  to  affect  intelligence,  foresight,  self- 
control,  habits,  the  longevity  of  man,  and  family  affection, 
will  have  their  influence  upon  the  rate  of  interest.  The 
most  fitful  of  the  causes  at  work  is  probably  fashion.  This 
at  the  present  time  acts,  on  the  one  hand,  to  stimulate 
men  to  save  and  become  millionaires,  and,  on  the  other 
hand,  to  stimulate  millionaires  to  live  in  an  ostentatious 
manner.  Fashion  is  one  of  those  potent  yet  illusory  social 
forces  which  follow  the  laws  of  imitation  so  much  empha- 
sized by  Tarde,^  Le  Bon,^  Baldwin,^  and  other  writers. 
In  whatever  direction  the  leaders  of  fashion  first  chance  to 
move,  the  crowd  will  follow  in  mad  pursuit  until  the  whole 
social  body  will  be  moving  in  that  direction.  Sometimes 
the  fashion  becomes  rigid,  as  in  China,  a  fact  emphasized 
by  Bagehot ;  *  and  sometimes  the  effect  of  a  too  universal 
following  is  to  stimulate  the  leaders  to  throw  off  their  pur- 
suers by  taking  some  novel  direction  — which  explains  the 
constant  vagaries  of  fashion  in  dress.  Economic  fashions 
may  belong  to  either  of  these  two  groups,  —  the  fixed  or  the 
erratic.  Examples  of  both  are  given  by  John  Rae.^  It 
is  of  vast  importance  to  a  community,  in  its  influence  both 
on  the  rate  of  interest  and  on  the  distribution  of  wealth 
itself,  what  direction  fashion  happens  to  take.  For  in- 
stance, should  it  become  an  established  custom  for  million- 
aires to  consider  it  "disgraceful  to  die  rich,"  and  beheve 
it  de  rigiier  to  give  the  bulk  of  their  fortunes  for  endowing 
universities,  libraries,  or  other  public  institutions,  the  effect 
would  be,  through  diffusion  of  benefits,  to  lessen  the  dis- 

'  Social  Laws,  by  G.  Tarde,  English  translation,  New  York  (Mac- 
millan),  1899.     Also  Les  Lois  de  l' Imitation. 

^  The  Psychology  of  Socialism,  English  translation,  London  (T. 
Fisher  Unwin),  1899.     Also  The  Crowd. 

'  Social  and  Ethical  Interpretations  in  Mental  Development,  New 
York  (Macmillan),  4th  ed.,  1906. 

*  Physics  and  Politics,  Chap.  III. 

•  See   The  Sociological  Theory  of  Capital. 


334  THE  RATE  OF   INTEREST  [Chap.  XVII 

parities  in  the  distribution  of  wealth,  and  also  to  lower 
the  rate  of  interest. 

§  6 

From  what  has  been  said  it  is  clear  that  in  order  to  esti- 
mate the  possible  variation  in  the  rate  of  interest,  we  may, 
broadly  speaking,  take  account  of  the  following  three  groups 
of  causes:  (1)  The  thrift,  foresight,  self-control,  and  love  of 
offspring  which  exist  in  a  community;  (2)  the  progress 
of  inventions;  (3)  the  changes  in  the  purchasing  power 
of  money.  The  first  cause  tends  to  lower  the  rate  of  in- 
terest ;  the  second,  to  raise  it ;  and  the  third  to  affect  only 
the  nominal  rate  of  interest,  though  practically  it  usually 
produces  also  a  dislocation  in  the  real  rate  of  interest. 

Were  it  possible  to  estimate  the  strength  of  the  various 
forces  thus  summarized,  we  could  base  upon  them  a  pre- 
diction as  to  the  rate  of  interest  in  the  future.  Such  a 
prediction,  however,  to  be  of  much  value,  would  require 
more  painstaking  attention  than  has  ever  been  given  to 
existing  historical  conditions.  Without  such  a  careful  in- 
vestigation, any  prediction  is  hazardous.  We  can  say, 
however,  that  the  immediate  prospects  for  a  change  in  the 
monetary  standard  are  toward  its  gradual  depreciation; 
that  a  change  in  thrift,  foresight,  self-control,  and  benevo- 
lence, if  it  occurs,  is  for  the  most  part  likely  to  intensify 
these  factors  and  thus  to  lower  the  rate  of  interest;  and 
that  the  progress  of  discovery  and  invention  seems  apt 
to  slacken  in  speed,  both  so  far  as  industrial  processes  are 
concerned,  and,  what  has  hitherto  been  of  more  conse- 
quence, so  far  as  the  discovery  of  exploitable  areas  is  con- 
cerned. It  is  true  that  the  new  chemical  agriculture  has 
the  same  effect  as  the  discovery  of  new  land.  It  is  con- 
ceivable, perhaps,  that  the  future  development  of  these 
methods  may  be  as  potent  as  was  the  discovery  and  ex- 
ploitation of  the  American,  Australian,  and  African  conti- 
nents, which  has  tended  to  keep  the  rate  of  interest  high. 


Sec.  6]  SUMMARY  335 

Yet  this  result  can  scarcely  be  regarded  at  present  as  prob- 
able. America  and  Australia  have  been  already  exploited 
to  a  large  degree,  and  within  another  generation  almost  the 
same  degree  of  exploitation  is  apt  to  occur  in  Africa.  If 
we  look  forward,  then,  beyond  the  present  lifetime,  unless 
some  invention  or  set  of  inventions  comparable  to  those 
of  steam  and  electricity  are  still  in  store  for  us,  we  see 
that  the  probable  improvement  in  thrift,  foresight,  self- 
control,  family  affection,  etc.,  and  the  slackening  in  the 
activity  or  economic  importance  of  inventive  processes,  are 
all  in  the  direction  of  lowering  the  rate  of  interest.  It 
may  of  course  happen  that  counter  currents  will  prove  the 
stronger.  There  is  certainly  danger  that  the  spirit  of  ex- 
travagance and  display,  a  spirit  which  we  have  seen  leads 
to  reckless  loans  and  high  interest,  will  become  a  national 
disease  as  it  did  during  the  decline  of  the  Roman  Em- 
pire. Only  time  can  tell  us  whether  or  not  we  shall  escape 
this  danger. 

So  far  as  the  effect  of  the  monetary  standard  on  the  rate 
of  interest  is  concerned,  the  prospect  of  depreciation  of 
gold  tends,  on  the  one  hand,  nominally  to  raise  the  rate  of 
interest,  but  practically  to  make  the  rate  of  interest  really 
not  only  low,  but  lower  than  it  otherwise  would  be.  With 
the  influx  of  gold  from  Colorado,  Alaska,  California, 
Australia,  and  latterly  Nevada,  and  with  the  resumption 
of  mining  in  South  Africa,  there  cannot  be  much  question 
that  gold  will  depreciate.^  This  result  will  tend  to  be 
intensified  by  the  fact  that  there  are  few  if  any  large  nations 
left  which  have  not  already  adopted  the  gold  standard  or 
which  are  at  all  likely  to  do  so,  and  thereby  mitigate  the  fall 
of  gold.  The  rate  of  interest  is  now,  on  ordinarily  safe 
loans  in  civilized  communities,  in  the  neighborhood  of 
4  per  cent.,  expressed  in  money.     We  may  surmise  that 

*  See  "Symposium,"  Moody's  Magazine,  December,  1905;  Byron 
W.  Holt,  The  Gold  Supply  and  ProsperUy,  N.  Y.  (Moody),  1907; 
also  "The  Depreciation  of  Gold,"  by  Professor  J.  P.  Norton,  Yale 
Review,  November,  1906. 


336  THE  RATE  OF  INTEREST  [Chap.  XVII 

through  much  of  the  present  century  this  rate  will  nomi- 
nally continue,  but  that  the  rate  of  interest  in  terms  of  "  com- 
modities" will  be  1  or  2  points  lower.  The  effect  of  these 
conditions  on  trade  and  on  the  relative  fortunes  of  stock- 
holders and  bondholders  has  been  stated  in  Chapter  XIV. 
The  rate  will  not  remain  perfectly  constant  but  will  tend 
gradually  to  rise  until  the  stringency  thus  produced  cul- 
minates in  a  commercial  crisis.  After  such  a  period  of 
liquidation,  the  same  process  of  rising  prices  with  high 
nominal  but  low  real  interest  will  begin  anew. 

A  discrepancy  of  1  or  2  points  between  the  rate  of  in- 
terest as  it  is  and  as  it  should  be  is  therefore  of  no 
trifling  importance.  Its  cumulative  effects,  although 
seldom  realized,  are  serious.  It  is  commonly  assumed  that 
the  rate  of  interest  is  a  phenomenon  confined  to  money 
markets  and  trade  centers,  and  the  public  approval  or 
disapproval  of  the  rate  usually  takes  its  cue  from  the 
sentiments  of  the  borrower.  If  "money  is  easy,"  he  is 
content. 

The  truth  is  that  the  rate  of  interest  is  not  a  narrow 
phenomenon  applying  only  to  a  few  business  contracts, 
but  permeates  all  economic  relations.  It  is  the  link  which 
binds  man  to  the  future  and  by  which  he  makes  all  his 
far-reaching  decisions.  It  enters  into  the  price  of  securi- 
ties, land,  and  capital  goods  generally,  as  well  as  into  rent, 
wages,  and  the  value  of  all  "  interactions."  It  affects 
profoundly  the  distribution  of  wealth.  In  short,  upon  its 
accurate  adjustment  depend  the  equitable  terms  of  all 
exchange  and  distribution. 


GLOSSARY 

[Consisting  of  definitions  of  technical  terms  used  in  this  book. 
Most  of  these  definitions  are  more  fully  discussed  in  The  Nature  of 
Capital  and  Income,  to  which  specific  references  are  therefore 
made.] 

Basis.  —  The  rate  of  interest  yielded  by  a  property  when  sold  at 
a  specified  price.     Capital  and  Income,  Ch.  XVI,  §  9. 

commercial,  of  a  security.  —  The  basis  corresponding  to  the  com- 
mercial value  of  the  security.   Capital  and  Income,  Ch.  XVI,  §  8. 

mathematical,  of  a  security.  —  The  basis  corresponding  to  the 
mathematical  value  of  the  security.  Capital  and  Income,  Ch. 
XVI,  §8. 

riskless,  of  a  security.  —  The  basis  corresponding  to  the  riskless 
value  of  the  security.     Capital  and  Income,  Ch.  XVI,  §  8. 
Capital.  —  Abbreviation    for    Capital   goods,    and    Capital  value. 
Capital  and  Income,  Ch.  V,  §  1. 

instruments.  —  (See  Capital  Wealth.) 

property.  —  A  stock  (or  fund)  of  property  existing  at  an  instant 
of  time.     Capital  and  Income,  Ch.  V,  §  1. 

wealth.  —  A  stock  (or  fund)  of  wealth  existing  at  an  instant  of 
time.  (Syn.  Capital  instruments.)  Capital  and  Income,  Ch. 
V,  §1. 

value.  —  The  value  of  a  stock  of  wealth  or  property  at  an  instant. 
It  is  found  by  discounting  (or  "capitalizing")  the  value  of  the 
income  expected  from  the  wealth  or  property.  Capital  and 
Income,  Ch.  V,  §  1. 
Capitalistic  method.  —  A  method  of  production  requiring  a  tem- 
porary reduction  in  the  income  from  specified  capital.  Ch. 
IX,  §  8. 
Caution,  coefficient  of.  —  The  ratio  of  commercial  value  to  mathe- 
matical value.  Capital  and  Income,  Ch.  XVI,  §  6. 
Chance,  of  any  event.  —  The  ratio  of  the  number  of  cases  in  which 
that  event  may  occur  to  the  total  possible  number  of  cases, 
when  all  the  cases  are  equally  probable.  Any  two  cases  are 
equally  probable  (to  any  particular  person  at  any  particular 
time)  if  the  person  has  no  inclination  to  believe  one  rather 
than  the  other  to  be  true.  (Syn.  Probability.)  Capital  and 
Income,  Ch.  XVI,  §  2. 

commercial  value  of.  —  The  value  which  the  chance  will  actually 
z  337 


338  GLOSSARY 

command  in  the  market.  It  is  equal  to  the  mathematical 
value  multiplied  by  the  coefficient  of  caution.  Capital  and 
Income,  Ch.  XVI,  §  6. 
mathematical  value  of.  —  The  product  of  the  value  of  the  price  at 
stake  multiplied  by  the  chance  of  winning  it.  Capital  and  In- 
come, Ch.  XVI,  §  5. 

Coefficient,  of  caution.  —  The  ratio  of  commercial  value  to  mathe- 
matical value.     Capital  and  Income,  Ch.  XVI,  §  6. 
of  probability.  —  The  ratio  of  mathematical  value  to  riskless 

value.     Capital  and  Income,  Ch.  XVI,  §  6. 
of  risk.  —  The  ratio  of  commercial  value  to  riskless  value ;  hence 
the  product  of  the  coefficient  of  caution  multiplied  by  the 
coefficient  of  probability.     Capital  and  Income,  Ch.  XVI,  §  6. 

Commercial  value  of  a  chance.  —  (See  Chance.) 

Commodities.  —  Movable  instruments  not  human  beings.  Capital 
and  Income,  Ch.  I,  §  2. 

Consumption.  —  (See  Services,  enjoyable  objective.) 

Desirability,  of  goods  (wealth,  property,  or  services).  —  The  in- 
tensity of  desire,  for  those  goods,  of  a  particular  individual 
at  a  particular  time  under  particular  circumstances.  (Syn. 
Utility.)  Capital  and  Income,  Ch.  Ill,  §  2. 
marginal,  of  a  specified  aggregate  of  goods.  —  Approximate 
definition :  The  desirability  of  one  unit  more  or  less  of  that 
aggregate,  or  the  difference  between  the  desirability  of  that 
aggregate  and  another  aggregate  one  unit  larger  or  smaller. 
Capital  and  Income,  Ch.  Ill,  §  4. 

Exact  definition :  The  limit  of  the  ratio  of  the  increment 
(or  decrement)  of  desirability  to  the  increment  (or  decrement) 
of  the  aggregate  when  the  last-named  increment  (or  decre- 
ment) approaches  zero.  (Syn.  Marginal  utility.)  Capital 
and  Income,  Appendix  to  Ch.  Ill,  §  1. 

Discount  curve.  —  A  curve  so  constructed  that,  if  one  of  its  or- 
dinates  represents  any  given  sum,  any  later  ordinate  will 
represent  the  "amount"  of  that  sum  at  a  time  later  by  an  in- 
terval represented  by  the  horizontal  distance  between  the 
ordinates ;  consequently  a  curve  such  that  any  earlier  ordinate 
will  represent  the  "present  value"  of  that  sum  at  a  time 
earlier  by  an  interval  represented  by  the  horizontal  distance 
between  the  ordinates.     Capital  and  Income,  Ch.  XIII,  §  1. 

Discounted  value.  —  (See  Value,  present.) 

Disservice.  —  A  negative  service.  An  instrument  renders  a 
disservice  when,  by  its  means,  an  undesirable  event  is  pro- 
moted or  a  desirable  event  prevented.  Capital  and  Income, 
Ch.  II,  §2;  VIII,  §  1. 


GLOSSARY  339 

Disutility.  —  Negative  utility.  (Syn.  Vndesir ability.)  Capital 
and  Income,  Ch.  Ill,  §  2. 

Earnings.  —  (See  Income,  earned.) 

Exchange.  —  The  mutual  and  voluntary  transfer  of  goods  (wealth, 
property,  or  services)  between  two  owners,  each  transfer  being 
in  consideration  of  the  other.     Capital  and  Income,  Ch.  I,  §  4 ; 

n,  §  3. 

Flow.  —  The   quantity  of  any  specified   thing  undergoing  any 
specified  change  during  any  specified  period  of  time.     Capital 
and  Income,  Ch.  IV,  §  1. 
Fund.  —  A  stock  of  wealth  or  property  or  its  value.     Capital  and 

Income,  Ch.  IV,  §  1. 
Goods.  —  A  term  to  include  wealth,  property  and  services.     Capi- 
tal and  Income,  Ch.  Ill,  §  1. 
Income.  —  Abbreviation   for  Income  services  and  Income  value. 
Capital  and  Income,  Ch.  VIII,  §  1. 

account.  —  Statement  of  specified  income  and  outgo,  whether 
from  capital  or  to  a  person.     Capital  and  Income,  Ch.  VIII,  §  2. 

earned,  by  any  capital.  —  Income  realized  plus  appreciation  of 
the  capital  (or  minus  its  depreciation) ;  i.e.  that  income 
which  a  given  capital  can  yield  without  alteration  in  its  value. 
If  interest  be  assumed  invariable  and  all  future  income  fore- 
known, this  definition  is  equivalent  to  another ;  viz.  the  uni- 
form and  perpetual  income  which  a  given  capital  might  yield ; 
but  the  equivalence  ceases  if  interest  varies  (see  Capital  and 
Income,  Appendix  to  Ch.  XIV,  §  1)  or  if  future  income  is  un- 
known. (Syn.  Earnings,  Standard  income.)  Capital  and 
Income,  Ch.  XIV,  §  4. 

enjoyable.  —  Income  which  consists  of  enjoyable  services.  Capi- 
tal and  Income,  Ch.  VII,  §  6. 

gross.  —  Sum  of  all  positive  income  elements.  Capital  and 
Income,  Ch.  VII,  §  1. 

individual.  —  The  income  from  the  entire  capital  of  an  individual. 
Capital  and  Income,  Ch.  VII,  §  7. 

money.  —  Income  which  consists  of  the  receipt  of  money.  Capi- 
tal and  Income,  Ch.  VII,  §  7 ;  IX,  §  5. 

natural.  —  Income  which  consists  of  services  not  obtained  by 
exchange.     Capital  and  Income,  Ch.  VII,  §  7 ;   IX,  §  5. 

net.  —  The  difference  between  gross  income  and  outgo.  Capital 
and  Income,  Ch.  VIII,  §  1. 

psychic.  —  Agreeable  conscious  experiences.  (Syn.  Subjective 
income.)     Capital  and  Income,  Ch.  X,  §  3. 

realized,  from  any  capital.  —  Its  actual  income,  i.e.  the  value  of 
its  actual  services.     Capital  and  Income,  Ch.  XIV,  §  4. 


340  GLOSSARY 

services,  of  any  capital.  —  The  flow  of  services  from  that  capital 
through  a  period  of  time.     Capital  and  Income,  Ch.  VIII,  §  1. 

social.  —  The  mcome  from  the  entire  capital  of  society.  Capital 
and  Income,  Ch.  VII,  §  7. 

standard.  —  (See  Income,  earned.) 

stream.  —  Synonym  of  Income.  Employed  to  emphasize  its 
duration  in  time. 

subjective.     (See  Income,  psychic.) 

value,   from  any  capital.  —  The   value   of   its   income-services. 
Capital  and  Income,  Ch.  VIII,  §  1. 
Instrument.  —  An    individual    article    of    wealth.     Capital    and 

Income,  Ch.  I,  §  1. 
Interaction.  —  An  event  which  is  a  service  of  one  capital  and  at 
the   same   time   a   disservice   of   another.     (Syn.   Interacting 
service,  Intermediate  service.  Preparatory  service.  Coupled  ser- 
vice.)    Capital  and  Income,  Ch.  IX,  §  2. 
Interacting  services.  —  (See  Interaction.) 
Intermediate  services.  —  (See  Interaction.) 

Interest.  —  The  product  of  the  rate  of  interest  multiplied  by  the 
capital-value.     Capital  and  Income,  Ch.  XIV,  §  4. 

explicit,  rate  of.  —  A  rate  of  interest  explicitly  contracted  for 
(in  contradistinction  to  implicit  interest).     Ch.  II,  §  1. 

implicit,  rate  of.  —  The  rate  of  interest  realized  on  any  invest- 
ment, the  exact  return  of  which  is  not  explicitly  contracted 
for,  but  is  left  to  be  determined  by  circumstances.     Ch.  II,  §  1. 

rate  of.  —  Many  meanings  are  given  below.  The  standard  mean- 
ing used  in  this  book  is  that  called  "rate  of  interest  in  the 
premium  sense  reckoned  annually."  Capital  and  Income, 
Ch.  XII,  §  4. 

rate  of.  —  In  the  price  sense :  The  ratio  between  the  annual  rate 
of  a  perpetual  annuity  and  the  equivalent  capital-value.  Cap- 
ital and  Income,  Ch.  XII,  §  2. 

The  rate  of  interest  is  said  to  be  reckoned  annually  if  the 
annuity  is  payable  in  annual  installments;  it  is  said  to  be 
reckoned  semiannually  if  the  annuity  is  payable  in  semiannual 
installments;  quarterly,  if  in  quarterly  installments;  continu- 
ously, if  payable  continuously. 

rate  of.  —  In  the  premium  sense :  The  excess  above  unity  of  the 
rate  of  exchange  between  the  values  of  future  and  present 
goods  taken  in  relation  to  the  time  interval  between  the  two 
sets  of  goods.  (Syn.  rate  of  interest  in  the  agio  sense.)  Capital 
and  Income,  Ch.  XII,  §  4. 

The  rate  of  interest  is  said  to  be  reckoned  annually  if  the 
two  sets  of  goods  are  one  year  apart.     This  is  the  standard 


GLOSSARY  341 

meaning  of  the  "rate  of  interest"  as  used  in  this  book.     It  is 

said  to  be  reckoned  semiannually,  if  they  are  a  half-year  apart ; 

quarterly,  if  three  months  apart;    continuously,  if  infinitesi- 

mally  apart. 
rate  of.  —  In  agio  sense :  (See  in  premium  sense.) 
rate  of.  —  Reckoned  annually,  semiannually,  quarterly,   continu- 
ously:   See  under  rate   of  interest   in  price  sense  and  rate  of 

interest  in  premium  sense, 
total.  —  The  difference  between  any  sum  and   its   "amount." 

Capital  and  Income,  Appendix  to  Ch.  XIII,  §  7. 
Investing.  —  Purchasing  the  right  to  remote  income.     Ch.  VII, 

§4.  ■ 

Labor.  —  Outgo  in  the  form  of  human  exertion.     Capital  and 

Income,  Ch.  X,  §  6. 
Land.  —  Wealth  which  is  part  of  the  earth's  surface.     Capital 

and  Income,  Ch.  I,  §  2. 
Mathematical  value  of  a  chance.  —  (See  Chance.) 
Option.  —  Any  one  of  a  number  of  income-streams  among  which 

an  individual  may  choose.     Ch.  IX,  §  L 
Outgo.  —  Negative  income.     Capital  and  Income,  Ch.  VIII,  §  1. 
Preparatory  services.  —  (See  Interaction.) 
Price.  —  A  ratio  of  exchange.     Capital  and  Income,  Ch.  I,  §  4. 
money.  —  The  quotient  found  by  dividing  the  money  exchanged 

for  goods  by  the  quantity  of  the  goods  themselves.     Capital 

and  Income,  Ch.  I,  §  4. 
Principal.  —  The  final  payment  on  a  bond  or  note,  supposed  to 

be  (but  not  always  in  fact)  equal  to  the  original  sum  "lent." 

Capital  and  Income,  Ch.  XIII,  §  7. 
Probability.  —  (See  Chance.) 
Production.  —  (See  Transformation.) 
Productive  process.  —  (See  Transformation.) 
Productivity,  physical.  —  The  ratio  of  the  quantity  of  services  of 

capital  per  unit  of  time  to  the  quantity  of  the  capital.     Capital 

and  Income,  Ch.  XI,  §  2. 
Productivity,  value.  —  The  ratio  of  the  value  of  services  of  capi- 
tal per  unit  of  time  to  the  quantity  of  the  capital.     Capital 

and  Income,  Ch.  XI,  §  2. 
Property  (or  property  rights) .  —  Rights  to  the  chance  of  future 

services  of  wealth.     Capital  and  Income,  Ch.  II,  §  3. 
right,  complete.  —  The  exclusive  right  to  all  the  services  of  an 

instrument.     Capital  and  Income,  Ch.  II,  §  10. 
right,  partial.  —  The  right  to  part  of  the  services  of  an  instru- 
ment, other  parts  belonging  to  other  owners.     Capital  and 

Income,  Ch.  II,  §  10. 


342  GLOSSARY 

Return.  —  When  used  alone,  "  return  "  signifies  the  value  of  the 
advantage  of  one  income-stream  compared  with  another  during 
any  particular  portion  of  its  course.     Ch.  VIII,  §  8. 

Return,  physical.  —  The  ratio  of  the  quantity  of  services  of  capi- 
tal to  the  value  of  the  capital.  Capital  and  Income,  Ch.  XI,  §  2. 
on  sacrifice,  rate  of.  —  That  rate  of  interest,  reckoning  by  which 
the  discounted  value  of  the  "  return  "  equals  the  discounted 
value  of  the  "  sacrifice."  Ch.  VIII,  §  8. 
value.  —  The  ratio  of  the  value  of  services  of  capital  to  the  value 
of  the  capital.     Capital  and  Income,  Ch.  XI,  §  2, 

Risk,  coefficient  of.  —  The  ratio  of  commercial  value  to  riskless 
value.  It  is  equal  to  the  product  of  the  coefficient  of  prob- 
ability multiplied  by  the  coefficient  of  caution.  Capital  and 
Income,  Ch.  XVI,  §  6. 

Riskless,  value.  —  The  value  which  a  thing  would  have  if  risk  were 
eliminated.     Capital  and  Income,  Ch.  XVI,  §  6. 

Sacrifice.  —  The  value  of  the  disadvantage  of  one  income-stream 
compared  with  another  during  any  particular  portion  of  its 
course.    Ch.  VIII,  §  8. 

Service.  —  An  instrument  renders  a  service  when,  by  its  means, 
a  desirable  event  is  promoted  or  an  undesirable  event  pre- 
vented.    (Syn.  Use.)     Capital  and  Income,  Ch.  II,  §  2. 

Services,  coupled.  —  (See  Interaction.) 

enjoyable    objective.  —  Services    received     directly     by   human 
beings,  and  not  (like  interactions)  merely  received  for  human 
beings  by  other  (objective)   capital.     (Syn.  [not  well  chosen] 
Consumption.)     Capital  and  Income,  Ch.  X,  §  1. 
intermediate.  —  (See  Interaction.) 
preparatory.  —  (See  Interaction.) 

Spending.  —  Purchasing  the  right  to  immediate  enjoyable  income. 
Ch.  VII,   §  4. 

Standard  income.  —  (See  Income,  earned.) 

Stock.  —  The  quantity  of  any  specified  thing  at  any  instant. 
(Syn.  Fund.)     Capital  and  Income,  Ch.  IV,  §  1. 

Time-preference,  rate  of.  —  The  excess  above  unity  of  the  ratio 
between  the  marginal  utility  (to  a  given  person,  under  given 
conditions,  at  a  given  time)  of  (say)  a  dollar's  worth  of  enjoyable 
income  available  at  any  time  and  a  dollar's  worth  of  enjoyable 
income  available  one  year  later.  It  follows  that  it  is  also  the 
excess  above  unity  of  the  ratio  between  the  quantity  of  the 
later  income  and  the  quantity  of  the  early  income  which  will 
exchange  for  each  other  (both  being  expressed  in  the  same 
standard,  as  dollars).     Ch.  VI,  §  1. 

Time-shape,  of  an  income-stream.  —  The  distribution  in  time  of  a 


GLOSSARY  343 

given  income-stream  as  expressed  by  the  relative  amoimts  of 
the  income  accruing  at  specified  periods.     Ch.  VI,  §  6. 
Transformation.  —  An  interaction  which  is  a  change  of  form  or 
condition  of  wealth.     (Syn.  Production,  Productive  process.) 
Capital  and  Income,  Ch.  IX,  §§  2,  3. 
Undesirabilitt.  —  Negative  desirabiUty.  (Syn.  Disutility.)     Capi- 
tal and  Income,  Ch.  Ill,  §  2. 
Utility  of  goods.  —  (See  Desirability.) 

Value.  —  The  value  of  goods  (wealth,  property,  or  services)  is 
the  product  of  their  quantity  multiplied  by  their  price.  Cap- 
ital and  Income,  Ch.  I,  §  6. 

commercial,  of  a  chance.  —  (See  Chance.) 

discounted.  —  (See  Value,  present.) 

mathematical,  of  a  chance.     (See  Chance.) 

money.  —  The  quantity  of  goods  multiplied  by  their  money 
price.     Capital  and  Income,  Ch.  I,  §  6. 

present.  —  The  present  value  of  any  given  future  goods  is  the 
quantity  of  present  goods  which  will  exchange  for  those  future 
goods.  (Syn.  Present  worth.  Discounted  value.)  Capital  and 
Income,  Ch.  XIII,  §  1. 

riskless,  of  a  chance.  —  (See  Chance.) 
Wealth    (in    its  broader  sense).  —  Material   objects   owned   by 
human  beings.     Capital  and  Income,  Ch.  I,  §  1. 

(in  its  narrower  sense).  —  Material  objects  owned  by  human 
beings  and  external  to  their  owners.  Capital  and  Income, 
Ch.  I,  §  2. 

article  of. —  A  single  object  of  wealth.  (Syn.  Item  of  Wealth, 
Instrument.)     Capital  and  Income,  Ch.  I,  §  1. 

item  of.  —  (See  Wealth,  article  of.) 
Worth,  present.  —  (See  Value,  present.) 


APPENDICES 


Appendix  to 
Appendix  to 
Appendix  to 
Appendix  to 
Appendix  to 
Appendix  to 
Appendix  to 


Chapter  II. 
Chapter  IV. 
Chapter  V. 
Chapter  VII. 
Chapter  VIII. 
Chapter  XI. 
Chapter  XIV. 


Productivity  Theories 
Bohm-Bawerk's  Theory 
Appreciation  and  Interest 
First  Approximation 
Second  Approximation 
Third  Approximation 
Statistics 


APPENDIX  TO   CHAPTER   II 

Productivity  Theories 

§  1  (to  Ch.  II,  §  6) 

Mathematical  Proof  that  the  Rate  of  Net  Income  from  Reconstituted 
Capital  is  equal  to  the  Rate  of  Interest  employed  in  valuing  the  Ele- 
ments of  which  that  capital  is  composed. 

That  the  ratio  of  the  net  income  from  the  machines  to  their 
capital-value  is  equal  to  the  rate  of  interest  used  in  calculat- 
ing the  value  of  each  individual  machine  is  a  necessary  truth 
and  may  be  shown  mathematically  as  follows :  — 

For  simplicity,  let  us  assume  that  each  machine  yields  its 
income  in  a  single  item  at  the  end  of  each  year.  If  a  machine 
when  new  is  to  last  m  years  and  yields  a  certain  annuity  of  a 
dollars  each  year,  the  value  {v^  of  this  machine  is  found  by 
discounting  the  terminable  annuity  of  a  dollars  for  m  years  at 
a  rate  of  interest  i.    This  value  will  be 

The  gross  annual  income  of  a  plant  consisting  of  m  machines 
will  be  ma.  The  net  income  of  the  plant,  assuming  that  one 
machine  wears  out  and  is  replaced  annually,  will  be  found  by 
deducting  from  this  gross  income  the  cost,  Vi,  of  a  new  machine. 
This  annual  net  income  =  ma  —  Vi. 

The  value  of  the  plant  of  m  machines  can  now  be  found 
by  discounting  the  future  income  which  the  plant  will  yield. 
Let  us  assume  that  the  plant  is  ''kept  up"  for  n  years, 
after  which  it  is  allowed  to  run  down  until  exhausted.  The 
period  of  running  down  will  be  m  years,  the  life  of  the  newest 
machine.  We  assume,  of  course,  that  whether  kept  up  or  run- 
ning down,  the  plant  yields  for  each  machine  a  dollars  annu- 
ally. Under  these  conditions  the  value  of  the  plant  is  the 
discounted  value  of  two  series  of  income :  (1)  n  years  of  income 
of  ma  —  Vi  per  year,  while  the  plant  is  kept  up,  and  (2)  m  years 
of  income  which   gradually  shrinks  from  ma  the   first  year 

347 


348 


APPENDIX   TO  CHAPTER   II 


when  all  the  machines  are  in  use,  to  (m~l)a  the  second  year, 
after  one  machine  has  dropped  out,  {m  —  2) a  the  third,  etc., 
to  a  in  the  mih.  year,  after  which  time  the  plant  will  cease  to 
exist.  We  have,  then,  the  present  value  of  ma  —  Vi  for  each 
of  n  years,  and  the  present  value  for  m  more  years  of  ma, 
(m  — l)a,  (m  — 2)a, •••a.  The  present  value  of  these  succes- 
sive sums  is  evidently 


Vma 


■V 


[ 


1  +  i 


ma 


i  + 


ma—  Vi 


(1  +  iy 

(m  —  l)a 


+  •••  + 


ma  —  Vi 


(1  +  0"+^    (1  +  0 


which  may  also  be  written 


n+2 


+ 


(1  +  0"_ 
+ 


+ 


a 


(1  +  i)"+" 


(ma  —  Vi) 


+ 


a 


(1  +  0" 


1  +  i 

m 


(1  +  0^ 

m  —  1 


_l  +  i      (l+i)' 


+  •••  + 


+  •••  + 


(l  +  i)" 

1 
(1  + 1)'"_ 


+ 


(2) 


Of  the  two  terms  of  which  this  expression  consists,  the  first 
is  the  more  important  if  the  rate  of  interest,  i,  has  a  finite 
positive  value,  but  the  second  is  the  more  important  if  that 
rate  is  zero.  In  the  former  case,  the  longer  the  plant  is  kept 
up  {i.e.  the  larger  n  is)  the  smaller  will  the  second  term  be- 
come ;  for  the  divisor  of  this  second  term,  (1  +i)",  will  increase 
indefinitely  and  the  other  factors,  a  and  the  square  bracket, 
remain  constant.  Hence,  as  n  increases  indefinitely,  this  second 
term  becomes  more  and  more  negligible  and  approaches  zero  as 
a  limit.  That  is,  the  value  of  a  plant  whose  up-keep  is  indefi- 
nitely maintained  is  equal  to  the  first^  of  the  two  terms.  This 
first  term  becomes,  when  ?i  is  indefinitely  great,^ 


(ma  —  Vi)  - 


(3) 


which  expresses  the  value  of  the  plant.  In  other  words,  the 
value  of  the  plant  is  the  capitalization  of  its  annual  net  in- 
Vi.     Or,  again,  the  annual  income  ma  —  Vi  divided  by 


come,  ma 


the  value  of  the  plant  (ma  —  Vi)  -  will  equal  the  rate  of  interest  i. 

i 

1  For  proof,  see   The  Nature  of  Capital   and   Income,   Appendix  to 
Ch.  XIII,  §  3. 


PRODUCTIVITY  THEORIES 


349 


The  same  result  applies  to  a  plant  which  contains  more  or 
less  machines  than  m,  since  the  size  of  the  plant  will  affect  both 
income  and  capital  alike. 


§  2  (to  Ch.  II,  §  7) 

Discussion  of  the  Case  of  Zero  Interest  as  Applied  to  the  Valuation  of 

Reconstituted  Capital. 

The  case  of  a  zero  rate  of  interest  offers  a  peculiarity  not 
presented  under  ordinary  circumstances.  In  all  other  instances 
of  perpetual  up-keep,  the  net  income  capitalized  gives  the 
entire  capital-value.  This  was  shown  in  §  1  of  this  Appendix. 
But  in  the  case  of  zero  interest  the  proposition  is  not  true,  as 
may  best  be  shown  by  mathematics.  In  §  1  of  this  Appendix 
the  expression  for  the  value  of  a  plant  of  m  machines  to  be 
kept  up  for  n  years  and  then  allowed  to  run  down  during  m 
years  was  found  to  be 


ma 


Vi      ma  —  Vi 


L  i  +  i     {i  +  if 


+  •••4 


ma 


(m— l)a 

_(l  +  i)"+l    '     (1  +  i)''+2 


+ 


+  •••  + 


ma  —  Vi 
(1  +  0". 
a 


-I- 


(1  +  ?:)"+'"_ 


In  the  previous  section  it  was  assumed  that  i  was  finite  and 
positive,  from  which  it  followed  that  when  n  was  indefinitely 
great  the  second  square  bracket  became  negligible.  But  under 
our  present  assumption  that  i  is  zero,  the  term  is  not  negligible ; 
on  the  contrary,  it  is  the  first  square  bracket  which  now  van- 
ishes. To  show  this  we  observe  that  formula  (1)  of  §  1, 
giving  the  value  of  each  machine,  reduces,  when  i  =  0,  to 


_a  a 
""11^ 
=  ma. 


+  - 


whence 

ma  —  Vi  =  {i. 

Hence   the  first   term  in  equation  (2),  being   the  product  of 
ma  —  'Ui  (zero)  by  a  finite  number,  is  zero. 

The  second  term  of  (2)  reduces,  when  i  =  0,  to 


9l 


m  ,  m  —  1  ,  ,    1 ' 


or  a 


'm{m  +  1)' 


350  APPENDIX   TO  CHAPTER  II 

■which,  since  the  first  term  is  zero,  represents  the  entire  vahie 
of  the  m  machines.  The  result  is  now  independent  of  n.  If 
m  =  10,  this  expression  becomes  55  a.  The  value  of  such  a 
plant  is  then  fifty-five  times  the  annual  yield  of  each  machine. 
If  this  yield  is  $100,  its  value  is  $5500,  which  agrees  with 
the  calculation  in  the  text. 


APPENDIX  TO   CHAPTER   IV 

Bohm-Bawerk's  Theory 

§1  (toCh.  IV,  §2) 

Nature  of  Various  Means  —  Arithmetical,  Geometrical,  Harmonical,  etc. 

In  general,  a  mean,  d,  of  a  number  of  magnitudes,  a„  a^,  a^,  etc., 
is  defined  by  an  equation  connecting  these  magnitudes  and  a 
in  such  a  manner  that  if  all  of  the  magnitudes,  ai,  Oj,  a^,  etc. 
are  equal  to  each  other,  the  value  of  a  given  by  the  equation 
will  be  equal  to  each  of  them.  That  this  concept  applies 
to  the  arithmetical,  geometrical,  and  harmonical  means  is 
evident.  These  means  may  be  defined  by  the  following 
formulae,  where,  for  convenience,  the  number  of  elements, 
tti,  ttj,  etc.,  averaged  is  restricted  to  three.  This  restriction, 
which  may  be  very  readily  removed,  is  adopted  solely  for 
brevity. 

(1)  Arithmetical,  d  +  d-|-a  =  ai  +  a2  +  a3or  a  —  — ^ 

(2)  Geometrical,  d  d  d  =  ai  aj  ag  or  d  =  -^a^^a^z 

,^,  ^^  .,111111  3 

{6)  Harmonical,  -  +  --}--  =  —  +  —  4-_     or  a 


a     a     a     cu      tto     a.  Ill 

«!      aa      Oa 

The  weighted  arithmetical  mean  is  given  by  the  formula 

WjO,  +  w-ifx  +  WM  =  Witti  +  w^a^  -f-  ivMo  or  a  =  ■ 

where  the  "  weights  "  are  the  coefficients  iu„  lo^,  w^.  This  is 
the  mean  employed  by  Bohm-Bawerk  in  the  example  given, 
the  elements  averaged,  a^,  a^,  as,  etc.,  being  the  different  ages 
of  the  labor,  10  years,  9  years,  8  years,  7  years,  etc.,  and  the 
weights  being  the  amount  of  labor,  $20,  $20,  $5,  $5,  etc. 
The  formulae  for  both  the  geometrical  and  the  harmonical 
averages  may  also  be  modified  by  introducing  "  weights." 

351 


352  APPENDIX  TO  CHAPTER  IV 

By    varying    the    formula   we    may    evidently    invent  an 
infinite  number  of  new  kinds  of  means.      Thus  the  formula 

a  tto 


«  +  -.,     /^  =  «i  +  fT:   , 
J- +  Va  -"--l-vag 

defines   a   as   a   sort   of    mean,   though   a   complicated   (and 
unsymmetrical)  one,  of  ai,  a2,  a^. 

§  2  (to  Ch.  IV,  §  2) 
Case  Illustrating  Futility  of  Measuring  Average  Production  Period. 

Bohm-Bawerk's  chosen  concept,  which  was  doubtless  adopted 
purely  for  convenience,  that  a  given  application  of  labor  will 
yield  its  return  in  a  single  sum  all  at  once,  is  far  too  simple 
to  cover  the  facts  as  actually  found.  On  the  contrary,  both 
the  labor  of  forming  instruments  and  their  return  are  spread 
over  a  considerable  period  of  time.  This  distribution  in  time 
may  take  any  form,  and  some  of  its  forms  would  render  use- 
less the  simple  arrangement  of  Bohm-Bawerk  of  production 
periods  into  a  series  of  varyhig  duration. 

Suppose,  to  take  an  extreme  case,  that  a  particular  applica- 
tion of  labor  issues  in  two  items  of  income,  namely :  $5  ten  years 
after  date,  and  $100  one  hundred  years  after  date;  while  another 
application  of  labor  issues  in  only  a  single  item  worth  $15 
in  twenty-five  years.  In  this  case  it  becomes  impossible  to  call 
one  of  the  production  periods  longer  than  the  other ;  for  whereas 
the  second  is  definitely  25  years  long,  the  first  may  be 
measured  as  any  period  between  10  and  100  years,  according 
to  the  method  employed  for  averaging  10  and  100.  Moreover, 
it  is  not  true  that  one  of  the  alternatives  will  be  chosen  if  the 
rate  of  interest  is  high,  and  the  other  if  the  rate  of  interest 
is  low,  as  would  be  the  case  if  they  were  subject  to  Bohm- 
Bawerk's  series.  The  application  of  labor  which  issued  in 
the  $5  and  $100  would,  oddly  enough,  be  the  most  economical 
if  the  rate  of  interest  were  either  very  high  or  very  low, 
whereas  the  other  alternative  would  be  chosen  in  case  the 
interest  were  at  a  more  moderate  rate.  Thus,  if  the  rate  of 
interest  were  5%,  the  present  value  of  the  $15  due  in  25 
years  would  be  $4.43,  and  that  of  the  two  items,  $5  in  10 
years  and  $100  in  100  years,  would  be  $3.83.  On  the  other  hand, 
if  the  rate  of  interest  were  1  %,  the  value  of  the  $5  and  $100 
alternative  would  be  $11.70  and  of  the  $15  alternative  $41.28. 


BOHM-BAWERK'S  THEORY  353 

Again,  if  the  rate  of  interest  were  25  %,  the  value  of  the  $5  and 
$100  would  be  $0.06  and  of  the  $15  alternative,  $0.54.  Hence, 
if  the  rate  of  interest  is  5%,  the  $15  alternative  will  be  prefer- 
able, whereas  if  the  rate  of  interest  is  either  1%  or  25%,  the 
other  alternative  will  be  chosen. 

§  3  (to  Ch.  IV,  §  3) 

Showing  how  Periods  of  Production  which   are   Relatively  Long  but 

Unproductive  are  Eliminated. 

That  long  processes  (assuming  their  length  to  be  measur- 
able) are  more  productive  than  short  processes  is,  as  Bohm- 
Bawerk  says,  a  general  fact,  not  a  necessary  truth.  The  reason 
lies  in  selection.  It  is  not  true  that,  of  all  2')ossihle  produc- 
tive processes,  the  longest  are  the  most  productive  ;  but  it  is 
true  that,  of  all  productive  processes  actually  employed,  the 
longest  are  also  the  most  productive.  No  one  will  select  a 
long  way  unless  it  is  at  the  same  time  a  better  way.  All  the 
long  but  unproductive  processes  are  weeded  out.  The  follow- 
ing illustration  will  make  the  process  clear : 

Suppose  that  by  means  of  100  days'  labor  invested  to-day 
we  can  obtain  a  product  of  100  units  one  year  hence,  or  of  250 
two  years  hence,  of  50  three  years  hence,  of  300  four  years 
hence,  of  250  five  years  hence,  of  320  six  years  hence,  of  100 
seven  years  hence,  of  300  eight  years  hence,  etc.,  —  a  series 
which  we  take  quite  at  random.  Out  of  this  series  of  choices 
there  will  be  eliminated  those  of  3,  5,  7,  and  8  years,  for 
each  of  these  is  outclassed  by  preceding  choices.  Thus, 
the  5-year  period  yielding  250  will  be  overshadowed  by  the 
4-year  period  yielding  300 ;  for  this  prospective  return,  being 
not  only  larger  but  earlier,  will  have  a  higher  present  value. 
Eliminating,  then,  these  ineligible  cases,  we  have  left,  to 
choose  from,  the  1,  2,  4,  and  6  year  periods.  Of  these,  that 
one  will  be  chosen  of  which  the  return  will  have  the  highest 
present  value ;  and  the  present  value  will  depend  on  the  rate 
of  interest.  If  interest  is  at  5%,  it  will  be  profitable  to  in- 
vest the  100  days'  labor  so  as  to  mature  in  four  years.  AB 
is  the  discounted  value  of  300  at  5  %  for  four  years,  it  being 
found  by  the  discount-curve  BC  drawn  at  5  %  from  C.  Since 
this  curve  passes  above  the  tops,  C",  C",  C",  of  all  the  other 
vertical  lines,  this  present  value  (at  5%)  of  300  in  four  years 

will  be  the  maximum  of  the  present  values  of  all  the  returns, 
2a 


354 


APPENDIX  TO  CHAPTER  IV 


100,  250,  50,  etc.  But  if  the  rate  of  interest  sinks  to  2  %,  as 
indicated  by  the  discount-curve  B'C,  the  point  of  maximum 
return  is  shifted  forward  to  six  years ;  for  the  discount-curve 
B'C  at  2  %  drawn  through  C  now  passes  above  the  tops  (C, 
(7",  C",  etc.)  of  all  other  lines,  hence  a  six-year  period  will  be 
chosen.  If,  on  the  other  hand,  the  rate  of  interest  were  10%, 
a  similar  construction  would  show  that  the  two-year  period 
would  be  selected,  as  the  highest  discount-curve  would  then 
pass  through  C".  But  in  no  case  will  the  highest  discount  curve 
touch  the  top  of  one  of  the  short  lines,  100,  50,  250,  100. 


b' 



C 

0' 

B 

^ 

c" 

250, 

300 

250 

320 

300 

C." 

/ 

100 

50 

100 

A  1  2  i3  4,  5  G  7  S.years 

Fig.  25. 

§  4  (to  Ch.  IV,  §  4) 

Mathematical   Refutation  of  Bohm-Bawerk's   Claim   as    to    Ground  of 
Preference  for  Present  over  Future  Investment  of  Labor. 

Let  the  products  obtainable  by  processes  of  1,  2,  3,  etc. 
years  be  pi,  jh,  Ihj  stc,  and  the  "  marginal  utilities  reduced  in 
perspective  "  beginning  in  1888  be  Wj,  tig,  U3,  etc.     Then, 

A   MONTH'S   LABOR   AVAILABLE 


In   1888   YIELDS 

In  1889  YIELDS 

For  the 

economic 

period 

Units  of 
product 

Marginal 

utility 
reduced 
in  persp. 

Amount  of 

value  of 

entire 

product 

Units 

Mar^. 
utility 

Value 

1888 
1889 
1890 
1891 
etc. 

Pi 
P2 
Pi 
Pi 

etc. 

Ml 
W2 
M3 
M4 

etc. 

PlUi 
P-zUi 
P3U3 
PiUi 

etc. 

Pi 

P2 
P3 

etc. 

«1 
u-z 

Us 

etc. 

P1U2 
P2U3 

P3Ui 

etc. 

B6HM-BA WEEK'S  THEORY  355 

We  shall  show  that  the  labor  available  in  1888  is  more  valu- 
able than  that  in  1889,  provided  only  m^  >  Uj  >  Mj  >  «<,  etc. ; 
that  is,  that  the  maximum  of  the  first  series  of  pu'?,,  relating 
to  1888,  is  greater  than  the  maximum  of  the  second  series, 
relating  to  1889  (assuming  of  course  that  maxima  exist).  To 
prove  this,  select  the  maximum  of  the  second  series.  Sup- 
pose it  to  be  p^^l^.  This  is  necessarily  less  than  p^u^  in  the 
first  series ;  for  since  1^4  <  u^  by  hypothesis,  it  follows  that 
J93W4  <  p3«3.  That  is,  there  necessarily  exists  in  the  first  series 
a  term  greater  than  the  greatest  term  in  the  second  series. 
A  fortiori  must  the  greatest  term  in  the  first  series  exceed  the 
greatest  in  the  second  series.  In  other  words,  the  value  for 
1888  exceeds  that  for  1889,  provided  only  the  marginal  utili- 
ties descend,  whether  or  not  the  productivities  ascend. 


APPENDIX   TO    CHAPTER   V 

Appreciation  and  Interest 
§  1  (to  Ch.  V,  §  2) 

History  of  Theory  of  Appreciation  and  Interest 

Investigation  shows  that  the  present  writer  was  by  no  means 
the  first  to  conceive  the  relation  between  appreciation  and 
interest.  Apparently  the  earliest  was  the  anonymous  author^ 
of  a  remarkable  pamphlet  entitled ;  *'  A  Discourse  Concern- 
ing the  Currencies  of  the  British  Plantations  in  America," 
Boston,  1740  (reprinted  in  the  Economic  Studies  of  Amer- 
ican Economic  Association,  1897).     He  writes  :  — 

"  The  Arguments  current  amongst  the  Populace  in  favour  of  Paper 
Money,  are, 

"I.  In  most  of  the  Paper  Money  Colonies  one  of  the  principal  Reasons 
alleged  for  their  first  Emissions  ;  was,  to  prevent  Usurers  imposing  high 
Interest  upon  Borrowers,  from  the  Scarcity  of  Silver  Money.  It  is  true, 
that  in  all  Countries  the  increased  Quantity  of  Silver,  falls  the  Interest  or 
Use  of  Money  ;  but  large  Emissions  of  Paper  Money  does  naturally  rise 
the  Interest  to  make  good  the  sinking  Principal :  for  Instance,  in  the 
Autumn,  A.  1737,  Silver  was  at  26s.  to  27s.  per  Ounce,  but  by  a  large 
Rhode  Island  Emission,  it  became  in  Autumn  1739,  29  s.  per  Oz.  this  is 
7  per  Cent.  Loss  of  Principal,  therefore  the  Lender,  to  save  his  Principal 
from  sinking,  requires  13  per  Cent,  natural  Interest  (our  legal  Interest 
being  6  per  Cent.)  for  that  Year.  In  Autumn  A.  1733,  Silver  was  22  s. 
per  Oz.  by  large  Emissions  it  became  27  s.  in  the  Autumn,  A.  1734;  is 
22  per  Cent,  loss  of  Principal ;  and  the  Lender  to  save  his  Principal ; 
requires  28  per  Cent,  natural  Interest  for  that  Year.  Thus  the  larger  the 
Emissions,  natural  Interest  becomes  the  higher ;  therefore  the  Advocates 
for  Paper  Money  (who  are  generally  indigent  Men,  and  Borrowers)  ought 
not  to  complain,  when  they  hire  Money  at  a  dear  nominal  Rate. 

"If  Bills  were  to  depreciate  after  a  certain  Rate,  Justice  might  be  done 
to  both  contracting  Parties,  by  imposing  the  Loss  which  the  Principal 
may  sustain  in  any  certain  Space  of  Time  (the  Period  of  Payment),  upon 
the  Interest  of  a  Bond  or  Price  of  Goods  :  but  as  Depreciations  are  uncer- 
tain, great  Confusions  in  Dealings  happen." 

1  Now  identified  as  the  physician,  William  Douglass. 

356 


APPRECIATION  AND  INTEREST  357 

John  Stuart  Mill  expressed  the  same  view/  as  have  also 
Robert  Goodbody,^  Jacob  de  Haas,^  and  Professor  John  B. 
Clark.*  A  principle  which  apparently  has  been  independently 
discovered  by  each  of  these  economic  students  and  quite  pos- 
sibly by  others,*  is  likely  to  be  of  some  importance. 

The  present  writer  published  in  1896  a  monograph^  in  which 
he  worked  out  the  relation  between  interest  and  appreciation 
in  quantitative  form,  its  application  to  special  cases,  its  statis- 
tical verification,  as  well  as  its  significance  in  the  theory  of 
interest  and  in  the  practical  problem  of  regulating  the  stand- 
ard of  deferred  payments.  The  major  part  of  the  material 
contained  in  this  monograph  is  reproduced  in  Chapter  V, 
Chapter  XIV,  and  this  Appendix. 

That  the  appreciation  or  depreciation  of  money  does  actually 


^Principles  of  Political  Economy,  Book  3,  Ch.  23,  §4.  [A  single 
paragraph.] 

2  Mr.  Robert  Goodbody,  Broker,  New  York,  has  for  years  in  his 
trade-letters  maintained  the  doctrine  that  the  rate  of  interest  is  high  when 
money  is  depreciating,  and  low  when  money  is  appreciating.  This  he 
discovered  about  1876,  when  the  decline  in  silver  was  attracting  attention. 
He  was  then  much  interested  in  the  higher  mathematics,  and  as  he  ex- 
pressed it,  "  accident  or  something  caused  me  to  differentiate  the  equation 
of  imports  and  exports  of  any  country,  not  with  respect  to  time,  but 
with  respect  to  the  variation  of  the  standard  of  value.  The  result  was 
that  I  found  that  the  fraction  formed  by  the  ratio  of  call  money  as  nu- 
merator and  time  money  as  denominator  was  smaller  when  the  money 
standard  was  falling  and  larger  when  it  was  rising." 

'"'A  Third  Element  in  the  Rate  of  Interest,''''  Journal  of  the  Eoyal 
Statistical  Society,  March,  1889.  [An  extended  discussion,  with 
statistics.  ] 

*"The  Gold  Standard  in  the  Light  of  Recent  Theory,"  Political 
Science  Quarterly,  September,  1895.  [Applied  to  the  bimetallic  con- 
troversy.] 

5  Mr.  Byron  "W.  Holt  has  cited  other  cases  in  which  the  relation  be- 
tween appreciation  and  interest  has  been  recognized.  In  his  paper 
entitled  "Interest  and  Appreciation  "  {Sotind  Currency,  Vol.  V,  No.  22, 
1898)  he  mentions  Senator  Jones  of  Nevada,  Professor  T.  N.  Carver,  now 
of  Harvard,  David  I.  Greene  of  Hartford,  and  Professor  H.  H.  Powers, 
formerly  of  Leland  Stanford. 

''"Appreciation  and  Interest:  a  study  of  the  influence  of  monetary 
appreciation  and  depreciation  on  the  rate  of  interest,  with  applications  to 
the  bimetallic  controversy  and  the  theory  of  interest."  Publications  of 
the  American  Economic  Association,  1896,  Vol.  XI,  No.  4,  pp.  331- 
442. 


358  APPENDIX   TO  CHAPTER  V 

influece  the  rate  of  interest  is  now  well  recognized  by  those 
who  have  given  attention  to  the  subject.^ 

§  2  (TO  Ch.  V,  §  3) 
Formula  Connecting  the  Rates  of  Interest  in  two  Diverging  Standards. 

In  order  to  state  the  general  relation  between  the  rates  of 
interest  and  appreciation  or  depreciation,  let  wheat  fall  in  gold 
price  (or  gold  rise  in  wheat  price)  so  that  the  quantity  of  gold 
which  would  buy  one  bushel  of  wheat  at  the  beginning  of  the 
year  will  buy  1  +  a  bushels  at  the  end,  a  being  therefore  the 
rate  of  appreciation  of  gold  in  terms  of  wheat. 

Let  the  rate  of  interest  in  gold  be  i,  and  in  wheat  be  j,  and 
let  the  principal  of  the  loan  be  D  dollars  or  its  equivalent  B 
bushels. 

Our  alternative  contracts  are  then  :  — 

For  D  dollars  borrowed,  Z)  +  Dt  or  2)(l  +  £)  dollars  are  due 

in  1  yr. 
For  B  bushels  borrowed,  B  +  Bj  or  B{\-\-j)  bushels  are  due 

in  1  yr. 

and  our  problem  is  to  find  the  relation  between  i  and  j,  which 
will  make  the  D(l  +  i)  dollars  =o  the  B(l  +j)  bushels.^ 
At  first,  D  dollars  ^  B  bu. 

At  the  end  of  the  year,       D  dollars  ^  JB  (1  +  a)  bu. 

Hence  at  the  end  of  the  year  i>  (1  +  ?)  dollars  ^B(l+a)  (1  +  i)bu. 
Since  D{l-\-i)  is  the  number  of  dollars  necessary  to  liqui- 
date the  debt,  its  equivalent  i?(l  +  a)  (1  +  0  is  the  number  of 
bushels  necessary  to  liquidate  it.  But  we  have  already  desig- 
nated this  number  of  bushels  by  ^(1  +j). 

1  See  Professor  Marshall's  testimony,  Indian  Currency  Jieport,  1899, 
Pt.  II,  p.  169;  Graziani,  Studi  sulIa  teoria  ddV  interresse,  Turin,  1898, 
pp.  120-29;  and  Joseph  F.  Johnson,  Money  and  Currency,  Boston  (Ginn), 
1905,  p.  158.  But  the  subject  has  as  yet  attracted  little  attention  in 
the  business  journals.  See  The  Bond  Record,  April,  1896  ;  also  the  first 
number  of  Moody''s  Magazine,  1905,  in  which  the  "  Symposium  "  and 
editorial  on  the  effects  of  increasing  the  supply  of  gold  are  partly  de- 
voted to  the  relation  between  monetary  depreciation  and  the  rate  of 
interest.  The  same  material  together  with  much  else  of  importance  is 
assembled  in  The  Gold  Supply  and  Prosperity,  by  Byron  W.  Holt,  New 
York  (Moody  Publishing  Co.),  1907.  See  also  J.  P.  Norton,  "The  Depre- 
ciation of  Gnkl,"  Yale  lieviexo,  1906-7,  pp.  298-306. 

*  The  symbol  <*  signifies  "  equivalent  to." 


APPRECIATION  AND   INTEREST  359 

Our  result,  therefore,  is  :  — 

Dollars  Bushels  Bushels 

at  the  end  of  one  year  D  (1  + 1)  0=  5  (1  -\-j)  =  S  (1  -f  a)  (1  +  i) ,  (1) 
which,  after  B  is  canceled,  discloses  the  formula  :  — 

l+i=(l  +  a)(l+0,  (2) 

or  j  =  i  -\-a-\-  ia.  (3) 

or  in  words :  The  rate  of  interest  in  the  relatively  depreciating 
standard  is  equal  to  the  stim  of  three  terms,  viz.  the  rate  of  inter- 
est in  the  appreciating  standard,  the  rate  of  appreciation  itself, 
and  the  product  of  these  two  elements. 

Thus,  to  offset  the  appreciation,  the  rate  of  interest  must  be 
lowered  by  slightly  more  than  the  rate  of  appreciation.^ 

We  may  introduce  depreciation  in  a  similar  manner.  Instead 
of  saying  gold  appreciates  at  the  rate  a,  relatively  to  wheat, 
we  may  say,  wheat  depreciates  at  the  rate  d,  relatively  to  gold.'* 
This  means  that  wheat  has  sunk  in  terms  of  gold  in  the  ratio 
1  to  1  —  d,  and  reasoning  similar  to  the  foregoing  shows  that 

1  +  t  =  (1  -  d)  (1  +j).  (4) 

Equations  (2)  and  (4)  may  be  conveniently  combined,  thus  : 

i+i^i  +  g  ^     1 

1  +  i         1         1-d'  (5) 

Since  — — -  is  the  ratio  of  the  value  of  gold  at  the  end  of  the 

year  to  its  value  at  the  beginning  (all  in  terms  of  wheat),  that 
is,  the  ratio  of  divergence  of  the  two  standards  expressed  in 

wheat,  while is  the  same  ratio  of  divergence  expressed 

in  gold,  and  since  l  +  i  is  the  "amount"  of  $1  put  at  interest 
for  one  year,  while  1  +J  is  the  "  amount "  of  one  bushel ;  we 
may  state  equation  (5)  as  follows :  — 

1  Professor  Clark  (Political  Science  Quarterly,  September,  1895)  im- 
plies that  1  %  appreciation  is  offset  by  less  than  1  %  reduction  of  interest. 
But  in  making  his  calculation  he  has  failed  to  "  compound."  The  numeri- 
cal illustrations  of  the  eighteenth  century  pamphleteer  (supra)  are  also 
erroneous.  E.g.  instead  of  28  7n  the  figure  should  be  20..32  %.  Professor 
Marshall  (Pri)iciples  of  Economics,  "Vol.  I,  3d  ed.,  p.  674)  gives  a  correct 
example,  designed  to  show  the  losses  from  a  fluctuating  currency. 

2  The  relation  between  d  and  a  is  (1  -f-  «)  (1  —  d)  =  1,  which  is  evi- 
dent from  equation  (5),  or  may  be  easily  shown  independently. 


360  APPENDIX   TO  CHAPTER  V 

The  ratio  of  divergence  between  the  standards  equals  the  ratio 
between  their  ^'amounts." 

This  is,  perhaps,  the  simplest  mode  of  conceiving  the  rela- 
tion, and  stress  is  laid  upon  it,  because  it  brings  into  promi- 
nence the  "  amount,"  or  ratio  of  future  payment  to  present 
loan,  a  magnitude  which  in  most  questions  of  interest  plays  a 
more  important  role  than  the  rate  of  interest  itself. 

Equation  (5)  gives  the  relation  between  i  and  j  in  terms  of 
a  or  d.  From  it  follows  the  value  of  j  in  terms  either  of  i  and 
a  or  of  i  and  d,  and  also  the  value  of  i  in  terms  either  of  j  and  a 
or  of  j  and  d,  thus :  — 

1+j  _l  +  a  _     1  /f-x 

TVi~~i~      -nd'  ^^> 

i  -A-  d 
whence  j  =  i  +  a  +  ia  =  —^ —  .  (6) 

or  i:=j-(j-  id  =  -i^^.  (7) 

It  follows  that  j  exceeds  i  by  more  than  the  rate  of  appre- 
ciation, which  in  turn  is  more  than  the  rate  of  depreciation 
{i.e.,  j—i>a>d). 

§  3  (to  Ch.  V,  §  4) 

Formulae,    when  Rates  of  Interest  and  of  Appreciation  are  Reckoned 

oftener  than  Yearly. 

In  case  we  take  the  half-year  instead  of  the  year  as  the  inter- 
val for  compounding  the  rates  of  interest  and  of  appreciation, 
it  may  readily  be  shown  that  the  formula 

1  +j  =  (1  +  i)  (1  -f  a)  gives  place  to 

whence  it  also  follows  that  instead  of  j  =  i-\-a-\- ia,  we  have 
the  relation 

ia 

In  case  the  interest  and   appreciation  are  compounded  quar- 
terly, the  formula  becomes 

ia 


APPRECIATION  AND  INTEREST  361 

and  so  on.  At  the  limit,  when  the  rates  of  interest  and  appre- 
ciation are  reckoned  continuously,  the  last  term  vanishes  and 
the  formula  becomes  simply  j  =  i  -{-  a. 

§  4  (to  Ch.  V,  §  5) 
Case  of  Partial  Payments. 

First,  consider  the  case  in  which  no  interest  is  paid  until  the 
end  of  the  term  of  years.  Let  us  suppose,  for  instance,  a 
savings  bank  which  receives  $100,  gold  standard,  and  repays 
the  depositor  in  five  years  at  5  %  compound  interest.  Let 
there  be  an  alternative  standard,  say  wheat,  worth,  at  the 
beginning  of  the  loan,  $1  per  bushel;  but  suppose  that,  in 
terms  of  wheat,  gold  is  known  to  appreciate  constantly  by  1  % 
per  annum.  What  would  be  the  rate  of  interest  in  terms  of 
wheat?  If  the  repayment  were  to  be  made  in  one  year,  the 
equivalent  of  the  5  %  would  be  a  rate  of  interest  in  terms  of 
wheat  of  6^^  %,  since  the  "amount"  of  a  dollar  of  gold  put  at 
interest  one  year  would  be  $1.05,  and  this  would  be  worth,  in 
bushels  of  wheat,  1.05  multiplied  by  1.01,  or  1.06^^^  bushels. 

This  result,  6^^tj%,  is  as  true  for  a  series  of  years  as  for 
one  year.  This  may  be  seen  by  separating  the  contract  into 
several  contracts  of  one  year  each.  If  we  imagine  deposited 
to-day  in  separate  savings  banks  $100  in  gold,  and  its  equiva- 
lent, 100  bushels  of  wheat,  they  will  amount  in  one  year 
respectively  to  $  1.05  at  5  %,  and  its  equivalent,  106.05  bushels 
at  &Yxf%-  ^^^  ^^^y  ^0^  regard  these  equivalent  amounts  as 
withdrawn,  but  immediately  redeposited  for  one  year.  Then, 
with  the  same  rate  of  interest  in  gold  and  the  same  relative 
appreciation,  we  shall  obtain  the  same  rate  of  interest  in  wheat, 
so  that  $105  and  its  equivalent,  106.05  bushels,  will  amount  in 
one  year  respectively  to  $110.25  at  5  %,  and  its  equivalent, 
112.47  bushels  at  Q^^%.  In  this  way  each  successive  pair  of 
"amounts,"  including  the  last,  will  be  equivalent. 

For  simplicity  we  have  considered  only  the  case  in  which  the 
debt  is  allowed  to  accumulate  to  the  end.  The  most  general 
ease,  however,  is  one  in  which  the  repayments  are  in  install- 
ments. 

Suppose,  as  before,  that  the  interest  in  gold  is  5  %  and  that 
gold  is  known  to  appreciate  1%  per  annum  relatively  to  wheat. 
A  farmer  mortgages  his  land  for  $1000,  or  its  then  equivalent, 


362 


APPENDIX   TO  CHAPTER  V 


1000  bushels  of  wheat,  and  agrees  to  pay  annually  the  interest 
and  such  parts  of  the  principal  as  he  can  save,  making  the 
repayment  complete  in  seven  years.  Our  problem  is  to  find 
that  rate  of  interest  in  wheat  which  will  make  the  contracts  in 
gold  and  wheat  equivalent  in  every  respect. 

The  solution  is  precisely  the  same  as  before,  viz.  ^^^%.  For, 
at  the  end  of  one  year,  the  farmer's  debt  amounts  to  $1050  or 
its  then  equivalent  1060.50  bushels.  Let  us  suppose  that  he 
finds  himself  able  to  pay,  not  only  the  interest,  $50,  but  also 
$50  of  the  "principal,"  that  is,  $100  all  together.  The  equiva- 
lent of  this  in  wheat  is  101  bushels.     Hence  he  can  either 

pay  $100  on         $1050.00        leaving  $950.00 
or        101  bu.  on     1060.50  bu.  leaving     959.50  bu. 

and,  since  the  "amounts"  $1050  and  1060.50  bu.  are  equiva- 
lent and  the  deductions  $100  and  101  bu.  are  equivalent,  the 
remainders  $950  and  959.50  bu.  must  also  be  equivalent;  in 
fact,  this  may  be  seen  directly,  since,  with  gold  appreciating 
1  %,  $950,  originally  worth  950  bu.,  becomes  worth  1  %  more 
or  959.50  bu. 

Thus  the  farmer's  remaining  debt  at  the  end  of  the  first  year 
is  the  same  whether  measured  in  wheat  or  gold,  and  since  the 
same  reasoning  applies  to  the  second  year,  third  year,  etc.,  the 
equivalence  remains  to  the  end  of  the  contract. 

It  is  worth  noting  here  that  the  $100  payment  in  gold  would 
be  regarded  as  consisting  of  half  "interest"  and  half  "princi- 
pal," whereas  the  equivalent  payment  in  wheat,  101  bu.,  will 
be  regarded  as  60.50  bu.  "interest,"  and  40.50  bu.  "principal." 

The  liquidation  of  the  contract  during  the  seven  years  may 
thus  be  supposed  to  take  place  in  either  of  the  following  equiva- 
lent ways :  — 

GOLD  STANDARD  (dollars) 


At  beginning 
In  1  year 
In  2  years 
In  3  years 
In  4  years 
In  5  years 
In  6  years 
In  7  years 


Intekest 


50.00 
47.50 
45.00 
40.00 
34.50 
27.50 
15.00 


Amount 


1050.00 
997.50 
945.00 
840-00 
724.60 
577.50 
315.00 


Payment 


100.00 
97.50 
145.00 
150.00 
174.50 
277.50 
315.00 


Principal 
Kemaining 


1000.00 
950.00 
900.00 
800.00 
690.00 
550.00 
300.00 
0.00 


APPRECIATION  AND  INTEREST 


363 


WHEAT  STANDARD  (bushels) 


At  beginning 
In  1  year 
In  2  years 
In  3  years 
In  4  years 
In  5  years 
In  6  years 
In  7  years 


Interest 


60.50 
58.05 
55.54 
49.87 
43.44 
34.97 
19.27 


Amount 


1060.50 
1017.55 
973.63 
874.11 
761.46 
613.03 
337.73 


Payment 


101.00 
99.46 
149.39 
156.09 
183.40 
294.57 
337.73 


Principal 
Remaining 


1000.00 
959.50 
918.09 
824.24 
718.02 
578.06 
318.46 
0.00 


In  these  two  tables,  every  entry  in  one  is  equivalent  to  the 
corresponding  entry  in  the  other  except  those  in  the  interest 
columns. 

We  thus  see  that  the  farmer  who  contracts  a  mortgage  in 
gold  is,  if  the  interest  is  j)roperly  adjusted,  no  worse  and  no  better 
off  than  if  his  contract  were  made  in  a  "wheat"  standard. 

This  principle,  that  debts  in  different  standards  are  equiva- 
lent if  the  rates  of  interest  in  the  two  standards  are  properly 
adjusted,  holds  true,  of  course,  no  matter  whether  the  "partial 
payments  "  are  large,  small,  or  none  at  all ;  no  matter  whether 
the  interest  payments  are  made  in  full,  in  part,  or  not  at 
all.  The  principals  in  the  two  standards  are  not  equivalent, 
except  at  the  beginning,  nor  are  the  annual  interest  sums 
equivalent;  but  the  excess  of  the  burden  of  interest  in  one 
standard  is  accompanied  by  a  deficiency  in  the  burden  of  the 
principal,  and  vice  versa. 


§  5  (to  Ch.  V,  §  5) 
Formulse  for  Cases  of  Compound  Interest  and  Partial  Payments. 

The  general  case  is  precisely  similar.  If  a  debt  in  either  of 
two  alternative  standards  is  to  accumulate  at  compound  interest, 
the  rates  of  interest  in  the  two  standards  must,  in  order  that 
the  contracts  in  each  shall  be  equivalent,  conform  to  the  for- 
mula, l+j={l  +  a)  (1  +  ?),  which  we  found  in  the  simpler 
case  of  a  one-year  debt. 

To  show  this,  resolve  the  contract  into  a  series  of  one-year 
contracts.  For  the  first  year  we  have,  by  formula  (1)  of  §  2 
above. 


364  APPENDIX   TO   CHAPTER  V 

Dollars  Bushels  Bushels 

due  due  due 

Dil  +  i)^B(l+j)  =  B(l  +  a)  (1  +  0 

In  the  second  year  the  same  formula  applies  except  that  in 
place  of  D,  the  principal  is  now  i)(l+i),  and  in  place  of 
B,  B  (1  +j)  or  JS  (1  +  a)  (1  +  0.  Making  these  substitutions 
in  the  formula,  we  obtain 

And  similarly  the  third  year, 

D{i  +  iy^B(i-hjy=Bii  +  ay{i-^iy, 

and  so  on.     Each  of  the  results  evidently  yields  the  formula 

l+i  =  (l  +  a)(l  +  0. 

If  a  debt  in  either  of  two  alternative  standards  is  to  be 
liquidated  in  *'  partial  payments,"  the  rates  of  interest  in  the 
two  standards  must,  in  order  that  the  contracts  in  each  may  be 
equivalent,  conform  to  the  same  formula. 

The  reason  is  simply  that  equivalent  payments  sub- 
tracted from  equivalent  "  amounts "  will  leave  equivalent 
remainders.  The  payment  in  any  year  forms  the  same  frac- 
tional part  of  the  "  amount "  in  the  two  standards.  We  may 
designate  this  fraction  at  the  end  of  the  first  year  by  /,  the 
second  year  by  /',  etc.,  and  we  have  the  following  results :  — 

End  of  First  Year 

Dollars  Bushels  Bushels 

Amount,  D  (l  +  i)o  B(l+j)=  B  (1  +  a)  (l  +  i) 

Payment,  /2)(l+0-  /^(l+j)=       /^(l+a)(l  +  0 

Remainder,    (1-/)  Z>  (l  +  j)  -  (1-/) -B  (l+j)=  (1-/)  B  (l  +  «)  (1  +  t) 

In  like  manner  the  unpaid  remainder  at  the  end  of  the 
second  year  can  be  shown  to  be 

Dollars  -  Bushels 

(i-f>)  (1-f)  D(i  +  iy^{i-f')  (i-f)B{i+jy 

Bushels 

=  (l-/')(l-/)5(l  +  ay(l+^)^ 

and  so  on  for  any  number  of  years.  Each  result  again  yields 
the  formula  (l+J)  =  (l+a)  (l  +  i).  Similar  reasoning 
applied  to  each  succeeding  year  yields  the  same  formula. 

The  case  in  which  there  are  no  partial  payments  is  met  by 
putting  /,  /',  equal  to  zero. 


APPRECIATION  AND  INTEREST 


365 


§  6  (to  Ch.  V.  §  5) 

Case  of  Separate    Payments    of    Interest  and  Principal  in  one  of  the 
Two  Standards  and  Equivalent  Payments  in  the  Other. 

Suppose  alternative  contracts  in  gold  at  5  %  and  wheat  at 
6-2^^%,  and  suppose  that  the  interest  in  the  gold  contract  is 
annually  paid  and  the  principal  redeemed  in  ten  years.  The 
following  tables  will  show  what  are  the  equivalent  operations 
in  the  wheat  standard. 

Liquidation  in  Gold  Standard,  Consisting  of  Annual  Interest  ($50) 
AND  Final  Principal  ($1000). 


At  beginning  (Dollars) 

In    1  year 

In    2  years 

In    3  years 

In    4  years 

In    5  years 

In    6  years 

In    7  years 

In    8  years 

In    9  years 

In  10  years 


Interest 

Amount 
Due 

Payment 

Principal 
Remaining 

— 



— 

1000.00 

50.00 

1050.00 

60.00 

1000.00 

60.00 

1050.00 

50.00 

1000.00 

60.00 

1060.00 

60.00 

1000.00 

60.00 

1060.00 

60.00 

1000.00 

60.00 

1060.00 

60.00 

1000.00 

60.00 

1050.00 

60.00 

1000.00 

60.00 

1050.00 

60.00 

1000.00 

60.00 

1050.00 

60.00 

1000.00 

60.00 

1050.00 

50.00 

1000.00 

60.00 

1050.00 

1060.00 

0.00 

Equivalent  Liquidation  in  Wheat  Standard  ;  Annual  Payments 
ARE  Less  than  Interest  (60.60  Bu.)  and  Final  Payment  More 
THAN  Principal  (1000  Bu.). 


At  beginning  (Bushels) 

In    1  year 

In    2  years 

In    3  years 

In    4  years 

In    6  years 

In    6  years 

In    7  years 

In    8  years 

In    9  years 

In  10  years 


Interest 

Amount 
Due 

Payment 

Principal 
Remaining 

— 

— 



1000.00 

60.60 

1060.50 

50.50 

1010.00 

61.10 

1071.10 

51.00 

1020.10 

61.72 

1081.82 

51.62 

1030.30 

62.32 

1092.62 

52.03 

1040.69 

62.96 

1103.55 

52.55 

1051.00 

63.69 

1114.69 

63.08 

1061.61 

64.22 

1125.73 

53.61 

1072.12 

64.86 

1136.98 

54.14 

1082.84 

66.51 

1148.35 

64.68 

1093.67 

66.17 

1169.84 

1169.84 

0.00 

366 


.APPENDIX   TO  CHAPTER  V 


If  we  suppose,  conversely,  that  interest  in  the  wheat  stand- 
ard is  annually  met  and  the  principal  redeemed  in  ten  years, 
the  equivalent  operations  in  the  gold  standard  will  be  as  shown 
below. 

Liquidation  in  "Wheat  Standard,  Consisting   of  Annual  Interest 
(60.50  Be.)  AND  Final  Principal  (1000  Bu.). 


At  beginning  (Bushels) 

In    1  year 

In    2  years 

In    3  years 

In    4  years 

In    5  years 

In    6  years 

In    7  years 

In    8  years 

In    9  years 

In  10  years 


Interest 


60.50 
60.50 
60.50 
60.50 
60.50 
60.50 
60.50 
60.50 
60.50 
60.60 


Amount 
Due 


1060.50 
1060.50 
1060.50 
1000.50 
1060.50 
1060.50 
1060.50 
1060.50 
1060.50 
1060.50 


Payment 


60.50 
60.50 
60.50 
60.50 
60.50 
60.60 
60.50 
60.60 
60.50 
1060.50 


Principal 
Remainino 


1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
1000.00 
0.00 


Equivalent  Liquidation  in  Gold  Standard  ;  Annual  Payments 
ARE  Greater  than  Interest  ($50)  and  Final  Payment  Less 
than  Principal  ($1000). 


At  beginning  (Dollars) 

In    1  year 

In    2  years 

In    3  years 

In    4  years 

In    6  years 

In    6  years 

In    7  years 

In    8  years 

In    9  years 

In  10  years 


Interest 

Amount 
Due 

Payment 

Principal 
Bemainino 

— 



— 

1000.00 

50.00 

10.50.00 

69.90 

990.10 

49.60 

1039.60 

69.31 

980.29 

49.01 

1029.30 

58.72 

970.58 

48.53 

1019.11 

58.14 

960.97   1 

48.06 

1009.02 

67.56 

951.46 

47.67 

999.03 

56.99 

942.04 

47.15 

989.19 

56.43 

932.76 

46.63 

979.39 

65.87 

823.62 

46.17 

969.69 

55.32 

914.37 

■;6.71 

960.08 

960.08 

0.00 

§  7  (to  Ch.  V,  §  5) 

Case  of  Separate  Payments  of  Interest  and  Principal  in  both  Standards. 

Let  us  next  compare  the  liquidations  in  the  two  standards 
by  the  simple  annual  payment  of  interest  in  each  (i.e.  $50  in 


APPRECIATION   AND   INTEREST  367 

the  gold  standard  and  60.50  bu.  in  the  wheat  standard,  not 
inter-equivalent)  and  in  ten  years,  final  payment  of  principal 
($1000  and  1000  bu.  not  inter-equivalent). 

In  this  case  the  individual  payments  in  the  two  cases  do  not 
correspond,  but  the  present  values  of  the  debts,  reckoned  at  any 
date  whatever,  are  always  identical.  Thus,  the  present  value, 
at  the  date  of  contract,  of  the  interest  and  principal,  separately 
computed,  at  6  %  and  62V  %  in  the  two  standards  respectively, 
will  be  :  ^  — 

Dollars  Bushels 

Present  value  of  all  interest  payments,  386.09  <  444.24 

Present  value  of  principal  due  in  10  years,  613.91  >  555.76 
Present  value  of  total,  1000.00  <>  1000.00 

If  the  present  values  were  computed  five  years  after  the  date 
of  the  contract,  and  the  "  amounts  "  of  past  interest  were  com- 
puted for  the  same  point  of  time,  the  items  would  be :  — 

Dollars  Bushels 

Interest  (present  value  and  amounts),  492.75  <  595.88 

Principal  (present  value),  783.53  >  745.50 

Total,  1276.28^1341.38 

The  two  sums  here,  though  not  equal  numbers,  are  equiva- 
lent magnitudes;  for  whereas  at  the  outset  $1  of  gold  and 
1  bushel  of  wheat  were  equivalent,  now,  after  five  years  of  an- 
nual appreciation  of  gold  relatively  to  wheat  at  the  rate  of  1  %, 
we  shall  find  $1  worth  (1.01)^  bushels,  or  1.051  bu.,  whence 
$1276.28  will  be  worth  1341.38  bushels. 

We  thus  see  that  it  would  be  just  as  much  of  a  hardship  to 
pay  the  higher  interest  in  wheat  during  the  whole  period  as  to 
pay  the  more  onerous  principal  in  gold  at  last. 

§  8  (TO  Ch.  V,  §  5) 

Case  of  Perpetual  Annuity. 

The  case  of  a  perpetual  annuity  may  be  given  special  consid- 
eration. As  is  well  known,  the  present  value  of  a  perpetual 
annuity  is  its  "  capitalized  "  value.  Thus,  if  the  rate  of  inter- 
est is  taken  at  5  %,  the  present  value  of  a  perpetual  annuity  of 
S50  per  annum  is  $1000.     Applying  the  same  principle  to  the 

1  The  symbol  <  is  here  used  for  "  is  less  than  the  equivalent  of,"  and 
>  for  "  is  more  than  the  equivalent  of." 


368  APPENDIX   TO  CHAPTER  V 

wheat  annuity  of  60.50  bushels  and  extending  the  previous 
reasoning,  we  find  that  the  two  annuities  are  equivalent. 

At  first  sight  this  seems  impossible,  since  62V  %  is  a  higher 
rate  of  interest  than  5  %.  This  is  true,  numerically,  and  it  is 
also  true  that  the  early  payments  of  60.50  bushels  are  actually 
more  valuable  than  $50.  But  after  a  certain  time  (in  this 
particular  case  19  years)  the  reverse  is  true.  The  19th  pay- 
ment of  $50  in  gold  is  worth  60.40  bushels,  while  the  20th  is 
worth  61.01  bushels.  That  is,  the  recipient  of  the  wheat  an- 
nuity has  at  first  a  slight  advantage  over  the  recipient  of  the 
gold  annuity,  which  ceases  and  becomes  a  slight  disadvantage 
after  19  years. 

To  derive  the  formula  for  the  time  at  which  the  relative 
values  of  the  two  annuities  become  reversed,  let  the  rate  of 
interest  in  gold  be  i,  in  wheat  j ;  let  the  two  annuities  be  Di 
and  Bj,  their  capitalized  values  being  D  and  B,  {DoB  at  the 
beginning),  and  let  x  be  the  number  of  years  in  which  Bj  is  as 
valuable  as  or  more  valuable  than  Di.     Then 

Bushels  Dollars 

At  the  end  of  x  years,  Bj  ^  Di 

At  the  end  of  a;  + 1  years,  Bj  <  Di 

and  since  we  know  that  in  x  years  D  o  5  (1  +•  a) "",  and  hence 
Di  =0  Bi  (1  +  a)^ ;  and  likewise  in  a:  +  1  years,  Di  o  Bi  (1  +  ay  +^, 
we  see  that  the  previous  inequalities  become  :  — 

Bushels  Bushels 

At  the  end  of  x  years,  Bj  ^  Bi(l  +  a)* 

At  the  end  of  a;  + 1  years,  Bj  <  Bi{l  +  ay-^^ 

which  may  be  combined  in  the  formula  :  — 

i{l  +  ay^j<i(l  +  ay  +  \ 
log.;-logt       ^      ^^ 
-Iog(l+a)  (8) 

That  is,  X  is  the  integral  part  of  the  number 

logj— logt 
log  (1 -fa)  ' 

Thus,  if  i  =  .05,  a  =  .01,  and  hence  also  j  =  .0605,  then 

logj  -  log  i  ^  2.7818  -  2.6990     .0828  ^  j^g  3 
log  (1  +  a)  .0043         ~  .0043 

Hence  x  =  19. 


APPRECIATION  AND  INTEREST 


369 


§  9  (to  Ch.  V,  §  5) 
Case  in  which  the  Kate  of  Appreciation  changes  each  Year. 

In  this  case  the  rate  of  interest  in  one  or  both  of  the  two 
standards  will  change  also. 

Beginning  with  a  numerical  illustration,  let  us  suppose  that 
a  syndicate  offers  the  United  States  government  an  alternative 
loan  in  gold  or  silver.  Let  it  be  known  that  100  gold  dollars 
will  remain  at  par  throughout  the  tirst  year,  but  in  two 
years  will  be  worth  150  silver  dollars,  that  is,  gold  will  "appre- 
ciate," in  the  second  year,  50  %  relatively  to  silver ;  also  that 
in  the  third  and  fourth  years  it  will  appreciate  10  %  and  5  % 
respectively.  We  shall  suppose  that  the  rate  of  interest,  if  the 
contract  be  in  gold,  is  3  %  for  each  year  of  the  contract. 

Our  problem  is  to  discover  what  will  be  the  rate  of  interest  in 
silver.  It  is  perhaps  already  evident  that  there  will  be  a  dif- 
ferent rate  for  each  year.  If  the  contract  were  made  for  one 
year  only,  the  rate  of  interest  in  silver  would  also  be  3  %,  since 
silver  remains  this  year  at  par  with  gold.  If  the  contract  (or 
any  unpaid  part  of  it)  were  then  renewed  for  a  second  year 
the  rate  of  interest  would  be,  by  formula  (3) :  — 

j  =  i  +  a  +  ai 
=  .03  +  .50  +  .015 
=  .545 

In  like  manner,  we  may  deduce  the  rate  of  niterest  in  each 
year,  with  the  following  results :  — 


Gold  Standard 

Appreciation 

Silver  Standard 

1st  year 

3% 

0% 

3% 

2d  year 

3% 

50% 

64r/o 

3d  year 

3% 

10% 

13A% 

4th  year 

3% 

5% 

8,\V/o 

etc. 

The  question  arises,  can  a  single  "average"  rate  of  interest 
be  substituted  for  the  above  irregular  series  of  rates  in  the  silver 
standard  ? 

We  answer  that  such  an  average  is  not  possible  if  the  debtor 
has  the  option  of  arbitrary  partial  payments.  If,  for  instance, 
the  average  were  20  %,  and  the  government  could  pay  off  at  any 
2b 


370  APPENDIX   TO  CHAPTER  V 

time,  it  would  evidently  be  tempted  to  refund  the  debt  at  the 
end  of  the  second  year,  to  which  the  lender  would  not  agree. 
If,  however,  the  conditions  as  to  repayment  are  stipulated  for 
in  advance,  an  average  can  easily  be  computed  on  the  prin- 
ciple of  present  values. 

Suppose  the  borrower  agreed  to  extinguish  the  debt  in  four 
years  by  paying  at  the  end  of  successive  years  20,  40,  30, 
and  10  millions  (these  to  include  ''interest").  The  present 
value  of  these  sums  is  66.321  millions,  which  is  therefore  the 
amount  of  the  loan  received  from  the  syndicate.  This  sum  is 
obtained  by  adding  the  present  values  of  several  payments. 
The  present  value  of  20  millions,  due  one  year  hence,  is 

20 

19.418  millions. 


1.03 
and  of  40  millions,  due  two  years  hence,  is 

^j^^gi^^  =25.136  millions; 

for  evidently  if  this  be  put  at  interest  for  one  year  at  3  %,  and 
for  the  next  at  54^^%,  it  will  amount  to  40  millions.  Like- 
wise the  third  and  fourth  payments  have  present  values  of 

30 

=  16.639  millions; 


(1.03)  (1.545)  (1.133) 

10 

(1.03)  (1.545)  (1.133)  (1.0815) 


=  5.128  millions. 


The  sum  of  these  four  present  values  is  66.321  millions. 
Now  if  we  compute  the  present  values  of  the  four  payments  on 
the  basis  of  a  uniform  "  average  "  rate  of  20.26  %  interest,  we 
obtain  the  same  sum,  thus :  — 

20 

=  16.631  millions 


(1.2026) 

40 
(1:2026?  =  27.659  millions 

30 
(1.2026)3  =  17.250  millions 

10 

(1.2026)* 

Total    =  66.321  millions 


=    4.781  millions 


APPRECIATION  AND  INTEREST 


371 


The  separate  present  values  are  here  fictitious,  that  is,  no  one 
of  them  is  the  actual  present  selling  price  of  the  future  payment 
to  which  it  refers,  but  the  deviations  so  offset  each  other  that 
their  sum  is  the  actual  present  selling  price  of  the  whole  set  of 
future  payments.  It  follows  from  principles  already  stated 
that  the  debt,  66.321  millions,  can  be  liquidated  by  precisely 
the  same  payments  (20,  40,  30,  and  10  millions)  whether  the 
interest  is  reckoned  separately  at  3,  54|,  13y\,  and  8ji\%,  or 
uniformly  at  20.26  %.  In  fact  the  details  of  the  bookkeeping 
in  the  two  eases  are :  — 


Date 


In  1  year 
In  2  years 
In  3  years 
In  4  years 


At  3,  54i,  13i%,  8A»3% 


( In  Millions) 


Interest 


1.99 

26.3.3 

4.61 

.75 


Amount 


68.31 
74.64 
39.25 
10.00 


Piivment 


20.00 
40.00 
30.00 
10.00 


Principal 


66.. 32 

48.31 

34.64 

9.25 

0.00 


At  20.26%  uniformly 


( In  Millions) 


Interest 


13.44 

12.11 

6.45 

1.68 


Amount 


79.76 
71.87 
38.32 
10.00 


Payment 


20.00 
40.00 
30.00 
10.00 


Principal 


66.32 

59.76 

31.87 

8.32 

0.00 


We  thus  see  that  20.26  %  is  the  "  average "  of  3,  541,  13^, 
and  S^^%,  in  the  sense  that,  reckoning  interest  by  this  "  aver- 
age," the  same  payments  will  cancel  the  same  debt  as  if  the 
separate  rates  were  used.  It  is  not  identical  with  the  arith- 
metical average,  which  is  19.74%. 

To  express  the  law  of  such  an  average  symbolically,  let 
us  suppose  that  the  rate  of  appreciation  of  one  standard 
in  terms  of  the  other  is  foreknown  to  be  Oi  the  first  year, 
0.2  the  second  year,  Og  the  third  year,  and  so  on ;  also,  to  be  as 
general  as  possible,  that  the  rates  of  interest  in  both  stand- 
ards are  variable,  being  in  the  appreciating  standard  ij  the 
first  year,  ij  the  second,  etc.,  and  in  the  depreciating  standard, 
ju  jii  6tc.  Let  the  final  settlement  occur  in  n  years.  Then,  as 
above,  we  may  regard  the  contract  as  equivalent  to  a  series  of 
one-year  contracts  successively  renewed  in  whole  or  in  part, 
the  only  difference  being  that  the  terms  are  all  made  in  advance. 
As  equation  (2)  of  §  2  applies  to  each  of  these  contracts,  we  have 


i+ji  =  (i  +  «0  (1  +  h) 

l+i2=(l+«2)    (1+^*2) 


l+j„=(l+«n)(l  +  ''n) 


(9) 


372  APPENDIX   TO   CHAPTER  V 

To  obtain  an  expression  for  the  average  rate  of  interest  in 
either  standard,  i.e.,  i^(ov  ja),  we  require  a  given  series  of  pay- 
ments, Di,  D2,  ...  Dn,  in  the  one  standard  (or  their  equiva- 
lent Bi,  B2,  ...  -B„,  in  the  other  standard).  The  aggregate 
present  value  of  these  payments,  reckoned  by  the  separate 
rates  of  interest,  h,  i^,  ...  ?„  (or  Jj,  jj ...  jn)  is 

+    /-I        .        .    N      /H        ,        .     X    +     •  •  •     4- 


l  +  ^l      {l  +  h){l  +  h)  '  '  (l+^•0(H-^;)..•(l  +  O 

(or  the  corresponding  expression  in  terms  of  JB's  and  /s). 
Now  the  "  average  "  rate  «'„  must  be  such  that  if  applied  to  the 
same  set  of  payments  it  will  produce  the  same  sum  of  present 
values ;  that  is,  ?'„  is  determined  by 

A     ■      A      ,         ,       A. 

l  +  4  +  (l  +  g^^  •*•  +(1 +  .•„)"-  (10) 

A  A  ,  A 

+  7^r~r~:TTT~r~^  +  •••  + 


l-f-i\^(l-hi,)(l-|-i-2)"^      ^(l-}-/0(l  +  i2)-(l  +  O' 

and  J„  is  determined  by  the  corresponding  formula  in  £'s 
and  /s. 

This  equation  has  only  one  real  and  positive  root  or  value 
of  ia.  It  can  readily  be  obtained  by  Horner's  method.^  We 
may  call  i„  and  j^  the  "present-worth-average"  of  i^,  i^,  ...  i^ 
and  ji,^  ...  j„  respectively.^ 

We  may  define  the  average  rate  of  appreciation  of  one  of 
the  two  standards  in  terms  of  the  other  as  that  rate  which 
would  connect  the  two  average  interest  rates  if  the  latter  were 
actual  (instead  of  averages  of  actual)  rates.^     That  is,  if  the 

1  For,  by  substituting  for r  the  single  letter  x,  and  for  - — — , :; r , 

etc.,  the  letters  xi,  Xo,  etc.,  the  equation  becomes  : 

Dix  +  D-iX^  +  •••  +  -D«ic"  =  DiXi  +  B-iXxXn  +  ...  +D„XiX2  •••  x„. 
In  the  example  given  previously  the  equation  becomes  :  — 
20  X  +  40  x2  +  30  x3  +  10  X*  =  66.321, 
the  required  root  of  which  is  x  =  .83155, 

which,  applied  to  x  =  :; r,  gives  ja  =  .2026. 

1  +Ja 

2  1  +  I'a becomes  the  "geometrical  average"  of  1  +iu  1  +  Z2,  etc., when 
Di  =  i)o=  ...  =Z>„_i  =  0. 

8  It  may  be  proved  that  this  definition  of  a„  satisfies  the  general  con- 
dition of  an  average,  viz.  that  Qa  reduces  to  ai,  a->,  etc.,  when  the  latter 
are  all  equal,  whether  t'l,  12,  etc.  (and  ji,  j-2,  etc.),  be  all  equal  or  not.  The 
proof  Is  left  to  the  reader. 


APPRECIATION  AND   INTEREST  373 

average  rates  of  interest  are  i„  and  J„,  the  average  appreciation, 
a„,  is  given  by  the  equation 

l+ja  =  (l  +  ia)    (l  +  tta); 
ja  -  4 

Thus,  as  in  the  example  given  above,  suppose  the  average 
silver  interest  is  20.26%  and  gold  interest  3%,  so  that 

.2026  -  .03  __ 
«-=  1  +  .03  =-^^^^' 
or  16.76  %.  This  average  is  not  identical  with  the  arithmetical 
average  of  0,  50,  10,  and  5%,  which  would  be  16.25%,  nor  is 
it  identical  with  that  rate  which,  if  uniform,  would  result  in 
four  years  in  the  same  divergence  between  silver  and  gold  as 
was  produced  by  the  four  successive  rates  0,  50,  10,  and  5%; 
this  would  be  14.70%. 


APPENDIX  TO   CHAPTER   VII 

First  Approximation 
(This  Appendix  should  be  read  as  a  whole  after  Chapter  VII.) 

§1 

As  the  preliminary  statement  of  the  theory  of  interest 
enunciated  in  Chapter  VII  contains  the  kernel  of  our  theory, 
it  will  be  worth  our  while,  before  proceeding  to  introduce  the 
various  complications  necessary  to  complete  it,  to  give  the 
first  approximation  a  full  mathematical  expression.  This 
mathematical  statement  will  serve  to  make  the  preceding 
results  clearer  and  more  sharply  defined.  It  will  also  serve 
to  demonstrate  the  important  fact  that  the  number  of  deter- 
mining conditions  is  exactly  equal  to  the  number  of  unknown 
quantities,  and  therefore  is  adequate  for  fully  determining 
those  unknown  quantities. 

Inasmuch  as  the  equations  are  necessarily  numerous  and 
complicated,  it  will  aid  the  reader  in  following  them  if  we 
break  the  argument  up  into  two  steps,  first  considering  an  arti- 
ficially simple  case  where  there  are  only  two  years  of  income 
to  be  considered,  and  then  passing  to  the  general  case  where 
there  are  any  given  number  of  years. 

Let  us  suppose,  therefore,  that  the  rate  of  preference  for 
this  year's  income  over  next,  in  the  case  of  each  individual, 
can  be  expressed  as  dependent  alone  on  the  amount  of  this 
year's  and  next  year's  income,  the  incomes  of  all  the  future 
years  being  regarded,  for  the  sake  of  argument,  as  fixed.  Sup- 
pose also  that  the  income  of  each  year  is  concentrated  at  one 
point,  say  the  middle  of  the  year,  making  the  two  such  points 
just  a  year  apart,  and  that  borrowing  and  lending  are  so  re- 
stricted as  to  affect  only  this  year's  and  next  year's  income. 

Let  /i  represent  the  rate  of  preference  for  this  year's  over 
next  year's  income,  for  individual  No.  1,  and  let  his  original 
endowment  of  income  for  the  two  years  be  respectively 
Ci'  and  r,".  This  original  income-stream,  c^',  Cj",  is  modified 
by  borrowing  this  year  and  repaying  next  year.     The  sum  bor- 

374 


FIRST  APPROXIMATION  375 

rowed  this  year  is  a*/,  the  value  of  which  is  yet  to  be  deter- 
mined. This  sum  is  therefore  to  be  added  to  the  present 
income  c/.  Next  year  the  debt  is  paid,  and  consequently  the 
income  c/'  for  that  year  is  reduced  by  the  sum  paid.  For  the 
sake  of  uniformity,  however,  we  shall  regard  both  modifica- 
tions algebraically  as  additions,  the  addition  a^'  to  the  first 
year's  income  being  a  positive  quantity,  and  the  addition, 
which  we  shall  designate  by  x/',  to  the  second  year's  income 
being  a  negative  quantity.  Thus,  if  $100  is  borrowed  this  year 
and  $105  repaid  next  year,  x^'  is  +  100  and  Xj"  is  —  105.  Thus 
the  first  year's  income  is  changed  from  c/  to  Ci  +  ^'  and  the 
second  year's  from  Cj"  to  Cj"  +  x/'.  By  this  notation  we  avoid 
the  necessity  of  employing  minus  signs.  Then  the  first  con- 
dition determining  interest,  namely,  that  the  rate  of  preference 
for  each  individual  depends  upon  his  income-stream,  is  repre- 
sented by  the  following  equation  :  — 

/i  =  F,(c,'  +  x/,  c/'  +  X,"), 

which  expresses  /i  as  a  function  of  the  income  of  the  two 
years.  In  case  the  individual  lends  instead  of  borrows,  the 
same  equation  may  be  taken  to  represent  the  resulting  relation 
between  his  rate  of  preference  and  his  income-stream  as  modi- 
fied by  lending ;  the  only  difference  is  that  in  this  case  the 
particular  value  of  x'  is  negative  and  of  x",  positive. 

In  like  manner,  for  individual  No.  2  we  have  the  equation 

f,  =  F,{c^+x.^,c.r-^x.r). 
For  the  third  individual, 

Ji  ^  -^3  \^3   ~r  ^'3  J  ^3    "I    ^'3  )■) 

and  so  on  up  to  the  last  or  nth  individual,  for  whom  the  equa- 
tion will  be 

/„  =  K  (cj  +  xj,  c„"  -f  c„"). 

These  n  equations  therefore  express  the  first  of  the  four  con- 
ditions mentioned  at  the  close  of  Chapter  VII. 

The  second  condition,  that  the  marginal  rates  of  preference 
of  the  n  different  individuals  for  present  over  future  income 
shall  be  equal  to  each  other  and  equal  also  to  the  rate  of  inter- 
est, is  expressed  by  the  continuous  eqviation :  — 

/i  =/2  =fs"'  =  •'•  =fn  =  i- 


376  APPENDIX  TO  CHAPTER  VII 

These  equations  hold  true,  as  we  saw  in  Chapter  VI,  because 
if  a  particular /should  be  greater  than  its  corresponding  i,  the 
individual  would  become  a  borrower,  and  if  /  should  be  less 
than  i,  he  would  become  a  lender.  In  the  former  case  the  effect 
of  his  borrowing  would  be  to  reduce  his  /  until  it  became  equal 
to  i.  In  the  latter  case  the  effect  of  his  lending  would  be  to 
increase  his  /  until  it  became  equal  to  i  likewise.  We  have, 
then,  as  a  result  of  borrowing  or  lending,  the  equation /=t, 
and  as  the  same  applies  to  every  individual,  all  the  /'s  are  equal 
to  i  and  therefore  to  each  other  also. 

The  third  condition,  namely,  that  the  market  must  be  cleared, 
or  that  the  loans  and  borrowings  must  be  equal,  is  expressed 
by  the  following  two  equations :  — 

aa'  +X2'  +...  +  ...+a;„'  =0, 
x^"  +  x,"  +  '"  +  "-+xJ'  =  0. 

That  is,  the  total  of  this  year's  borrowings  is  zero  (lendings 
being  regarded  as  negative  borrowings),  and  the  total  of  next 
year's  returns  is  likewise  zero  (payments  being  regarded  as 
negative  returns). 

The  fourth  and  last  condition,  that  for  each  individual  this 
year's  loans  and  next  year's  returns  discounted  are  equal,  is 
fulfilled  in  the  following  equations,  each  corresponding  to  one 
individual :  — 

^  II 


X    " 


§2 

We  now  proceed  to  compare  the  number  of  equations  with 
the  number  of  unknowns.     There  are  evidently  n  equations  in 


FIRST  APPROXIMATION  377 

the  first  set,  n  in  the  second,  2  in  the  third,  and  n  in  the  fourth, 
making  in  all  3?i  +  2  equations.     The  unknown  quantities  are 


Jij    J2>    /a;       •  *  *  )    "'  }    fn) 

or  n  unknowns, 

£Cl',    X2',Xs',       ...,     •..,     Xj, 

or  n  unknowns, 

Xy",Xi"  X^",      ...,      ...,     Xj\ 

or  n  unknowns. 

and  finally,  i, 

1  unknown. 

making  in  all  37i  +  1  unknowns. 

We  have,  then,  one  more  equation  than  necessary.  But  ex- 
amination of  the  equations  will  show  that  they  are  not  all 
independent,  since  any  one  equation  in  the  third  and  fourth 
sets  may  be  determined  from  the  others  of  those  sets.  Thus, 
to  determine  the  first  equation  of  the  third  set,  add  together 
all  the  equations  of  the  fourth  set.     The  addition  gives 

(x,'+x,'  +  x,'+  ...  +  ...  +a.:)+<+^^''+^3''+...  +  ...+^J'^o. 

In  this  equation  we  may  substitute  zero  for  the  numerator 
of  the  fraction,  as  is  evident  by  consulting  the  second  equation 
of  the  third  set.  Making  this  substitution,  the  above  equation 
becomes 

X,' +  X,' +  X,' -^  ...  +  ...  +xj=0, 

which  is  identical  with  the  first  equation  of  the  third  set. 
Since  we  have  here  derived  the  first  equation  of  the  third  set 
from  all  the  other  equations  of  the  third  and  fourth  sets,  the 
equations  are  not  all  independent.  It  follows,  therefore,  that 
of  the  3  n  +  2  equations,  one  may  be  dispensed  with  (namely,  any 
one  of  the  equations  of  the  third  or  fourth  sets),  so  that  there 
are  left  only  37i  +  l  indejmadent  equations,  which  are  there- 
fore exactly  equal  in  number  to  the  unknown  quantities  to  be 
determined.  There  are,  therefore,  just  sufficient  equations  to 
determine  those  unknown  quantities,  namely,  the/'s,  or  rates  of 
preference  for  different  individuals,  the  a;"s  and  a-"'s,  or  the 
loans  and  their  repayments,  and  finally,  i,  the  rate  of  interest. 

§3 

In  order  to  obtain  an  explicit  expression  for  i,  we  may  "  solve 
with  respect  to  i "  all  of  the  preceding  equations  that  can  be 


378  APPENDIX   TO  CHAPTER  VII 

so  treated.     Thus,  to  take  one  of  the  equations  from  the  third 

set,  namely,  Xi  -| i—  =  0,  it  is  evident  that,  solving  for  i,  this 

1+i 

equation  may  be  written 

1=  '  T 


To  interpret  this,  we  recall  that  a;/  is  a  sum  borrowed  this  year 
(say  $100)  and  thus  added  to  this  year's  income,  and  Xj",  being 
the  sum  "  added "  next  year,  and  hence  a  negative  quantity 

(say  —  105),  it  follows  that  —  Xi"  is  the  positive  quantity  (as  105) 

—  X  "                       (     105\ 
returned.      Hence ^  is  the  ratio  [  as )  of  the  sum  re- 

x{  \      lOOy/ 

turned    to    the    sum    borrowed,    or   the    ratio    of    exchange 

between   this    year's   and  next    year's   goods,    and '^- 1 

(  as  — —  —  1,  or  5  %  j  is  the  premium  above  par  of  the  rate  of 
exchange.     Since  this  premium  is  the  definition  of  the  rate 

of  interest,  the  equation  i  = ^ 1  is  merely  an  equation 

x^ 

of  definition. 

The  results  of  the  proposed  transformations  may  be  summa- 
rized as  follows  :  — 

=  F,(c/  +a;/,c/'-|-0=i^2(c2'+<C2"  +  a:2")=  -  =^n(etc.) 


_l  =z:^_i 


a;/  x.^  x^ 

These  three  equations  give  the  value  of  i,  subject  to  the  addi- 
tional condition :  — 

Xi-\-x^+  '"  +  •••  +xj  =  0, 

the  other  equation  of  the  same  type  as  the  last  being  omitted 
as  the  one  superfluous  equation.  The  equation  above  written 
could  be  itself  dispensed  with  by  substituting  in  the  previous 
equations  the  value  of  Xi  derived  from  it,  namely, 

-X.,' xj. 

These  equations  state  that  the  rate  of  interest,  under  the 
conditions  of  the  problem,  will  be  equal  to  the  rates  of  time- 
preference  for  all  the  individuals,  as  well  as  equal  also  to  a 


FIRST  APPROXIMATION  379 

certain  definite  function  of  the  income-streams  as  finally  de- 
termined by  the  loans  and  to  the  premium  of  exchange  of  this 
year's  income  in  terms  of  next  year's  income.  These  con- 
ditions, taken  together  with  the  condition  that  the  sums  lent 
must  be  equal  to  the  sums  borrowed — that  is,  that  the  rate  of 
interest  must  be  such  as  just  to  clear  the  market  — will  yield  a 
complete  determination  of  the  rate  of  interest,  which  is  the 
object  of  our  search. 

It  may  be  remarked  in  passing  that  the  first  of  the  three 
continuous  equations  given  above  is  closely  analogous  to  the 
third ;  in  fact,  the  first  may  be  called  the  subjective  proto- 
type of  the  third,  which  may,  in  like  manner,  be  called  the 
objective  expression  of  the  first.  The  third  equation  states 
the  definition  of  the  rate  of  interest  as  the  premium  in  the 
ratio  of  exchange  between  this  year's  and  next  year's  income, 
and  the  first  states  that  the  rate  of  interest  is  equal  to  the 
premium  in  the  relative  desirability  of  the  two.  It  is  not  diffi- 
cult to  express  the  analogy  algebraically  by  putting  the  /'s 
equal  to  the  excess  above  unity  of  the  ratio  between  the  mar- 
ginal desirability  of  this  year's  income  and  the  marginal  desir- 
ability of  next  year's  income. 

If  we  desire  only  to  obtain  the  simplest  expression  for  deter- 
mining i,  the  above  equations  may  be  condensed  still  further. 
The  first  continuous  equation  may  be  omitted  altogether. 
For,  to  omit  it  will  evidently  rid  us  of  as  many  unknown 
quantities  as  equations,  namely,  n.  Again,  since  the  third 
continuous  equation  is  evidently  nothing  more  than  a  defini- 
tion of  the  rate  of  interest,  we  may,  if  we  choose,  omit  the 

letter  i  and  employ  the  expression ^- 1  in  its  place.     We 

shall  then  have,  instead  of  the  three  continuous  equations 
above  expressed,  simply  the  following  continuous  equation:  — 

_^a 1=    —    ^ 1=Z    ...—    —    ^ 1 

=  i^„(c„'-f-a:„',c„"-f-cc„"). 

This  equation,  together  with  the  equation  for  clearing  the 
market,  a^i' -f  a-j' -i -|-x„'  =  0,  will  fully  determine  the  rate 


380  APPENDIX  TO  CHAPTER  VII 

of  interest.  But,  as  was  shown,  the  equation  for  clearing  the 
market  may  be  omitted,  if  we  iirst  obtain  from  it  the  value 
of  one  of  the  unknowns  it  contains,  say,  x^',  and  substitute  this 
value  in  the  previous  continuous  equation.  The  continuous 
equation,  so  amended,  will  then  of  itself  yield  a  complete  solu- 
tion of  our  problem. 

§4 

In  the  preceding  solution,  the  loan  transactions  were  sup- 
posed to  extend  over  two  years  only.  This  restriction  was 
made  in  order  that  the  mathematics  might  be  as  simple  as 
possible  in  our  first  formulation.  We  shall  now  remove  this 
restriction  and  proceed  to  the  case  in  which  more  than  two 
years  (let  us  say  m  years)  are  involved.  We  shall  assume,  as 
before,  that  the  ic's,  representing  loans  or  borrowings,  are  to 
be  considered  of  positive  value  when  they  represent  additions 
to  income,  and  of  negative  value  when  they  represent  deduc- 
tions. The  equations  in  the  first  set  will  now  be  in  several 
groups,  of  which  the  first  is : 

/a'=  F,.  (c^  +  X,',  c,"-\-  X,",  c,"<  +  X,'", ...  c^^-'-f-  x,^'-^), 

fj  =  F,.  (c„'  +  xj,  cj'  +  xj',  c,r  +  x:", . . .  c„(->  -f-  x^^-^). 

These  equations  express  the  rates  of  preference  of  different 
individuals  (//  of  individual  No.  1,  /j'  of  individual  No.  2,  etc.) 
for  the  first  yew's  income  compared  with  the  next.  To  ex- 
press their  preference  for  the  second  year's  income  compared 
with  the  next  there  will  be  another  group  of  equations,  namely : 

/i"  =  F,.  (c/'  -t-  X,",  c/"  +  xr,  -  c/-)  +  ar/"*'), 
/,"  =  F^.  (c,"+x,", c/'")  -f-  x,^'"^), 

/n"  =  F„,.  (c„"  +  xj\ c,/"'>  +  0.-,/"')). 

For  the  third  year  there  will  be  still  another  group,  formed 
by  inserting  "'""  in  place  of  «"",  and  so  on  to  the  m  — 1st 
year;  for  the  m  — 1st  year  is  the  last  one  which  has  any  ex 
change  relations  with  the  next,  since  the  next  is  the  mth  or  last 
year.  There  will  therefore  be  m  —  1  groups  of  equations,  and 
since  each  of  these  (m  —  1)  groups  contains  n  separate  equa- 
tions, there  are  all  together  n(m  —  1)  equations  in  the  entire 
set. 


FIRST  APPROXIMATION  381 

Turning  to  the  second  set,  we  first  observe  tliat  we  are  now 
compelled  to  assume  a  separate  rate  of  interest  for  each  year. 
The  rate  of  interest  connecting  the  first  year  with  the  next 
will  be  called  i\  that  connecting  the  second  year  with  the  next, 
i",  and  so  on  up  to  i^"'~'^\ 

Under  these  conditions  we  shall  find,  as  before,  that  the 
rates  of  time-preference  for  each  year  will  be  reduced  to  a 
uniform  level  for  all  the  different  individuals  in  the  com- 
munity, —  a  level  equal  to  the  rate  of  interest.  Algebraically 
expressed,  this  condition  is  contained  in  several  continuous 
equations,  of  which  the  first  is 

This  expresses  the  fact  that  the  rate  of  time-preference  of  the 
first  year's  income  compared  with  next  is  the  same  for  all 
the  individuals,  and  is  equal  to  the  rate  of  interest  between 
the  first  year  and  the  next.  A  similar  continuous  equation 
may  be  written  with  reference  to  the  time-preferences  and 
interest  as  between  the  second  year's  income  and  the  next, 
namely :  — 

*    —J\   =./2   =/3   =•••=/«  • 

Since  the  element  of  risk  is  supposed  to  be  absent,  it  does  not 
matter  whether  we  consider  these  second-year  ratios  as  the 
ones  which  obtain  in  the  minds  of  the  community  to-day, 
a  year  in  advance,  or  those  which  will  obtain  next  year ;  under 
our  assumed  conditions  of  no  risk,  these  are  necessarily 
identical. 

A  similar  set  of  continuous  equations  applies  to  time-ex- 
change between  each  succeeding  year  and  the  next,  up  to  that 
connecting  the  m  —  1st  and  the  mi\\  year.  There  will  therefore 
be  m  —  1  continuous  equations.  Since  each  continuous  equa- 
tion is  evidently  made  up  of  n  constituent  equations,  there 
are  in  all  w(m  —  1)  equations  in  the  second  set  of  equations. 

The  third  set  of  equations,  which  expresses  the  ''clearing 
of  the  market,"  will  be  as  follows :  — 

x,'  +  x^   +'--+x,^        =0, 


There  are  here  m  equations. 


382  APPENDIX   TO  CHAPTER  VII 

The  fourth  set  of  equations,  expressing  the  equivalence  of 
loans  and  repayments,  or  more  generally,  the  fact  that  for  each 
individual  the  total  "  additions "  to  his  income- stream,  alge- 
braically considered,  will  have  a  present  value  equal  to  zero, 
as  expressed  in  the  following  equation :  — 

^'  '^1  +  i'  "^  (l  +  i')(l  +  i")  +  '"  "•"  (l4.i')(l+i") ...  (l  +  i("-i)) 

=  0. 
Similar  equations  will  hold  for  each  of  the  n  individuals :  — 

3^3'+,-^  + -  =  0, 

1  -ft' 
making  in  all  n  equations. 

We  therefore  have  as  the  total  number  of  equations  the 
following :  — 

n(m  —  1)  equations  of  the  first  set 
w(m  —  1)  equations  of  the  second  set 
m  equations  of  the  third  set 

n  equations  of  the  fourth  set 

2  mn  +  m  —  n  equations  in  all. 

We  next  proceed  to  count  the  unknown  quantities.  First 
as  to  /'s :  for  individual  No.  1  these  will  be  //,  //',  •  •  •,  Z/™"^^  the 
number  of  which  is  m  —  1,  and  as  there  are  an  equal  number 
for  each  of  the  n  individuals  there  will  be  in  all  n(m— 1)  un- 
known /'s. 

As  to  x's,  there  will  be  one  for  each  of  the  7n  years  for  each 
of  the  n  individuals,  or  mn.  As  to  fs,  there  will  be  one  for 
each  year  up  to  the  next  to  the  last,  or  m  —  1.  In  short  there 
will  be 

n(m  —  1)  unknown  /'s, 
mn  unknown  a;'s, 
m  —  1  unknown  i's, 

or  2  mn  -f  m  —  n  —  1  unknown  quantities  in  all.  Comparing 
this  with  the  number  of  equations,  we  see  that  there  is  one 
more  equation  than  the  number  of  unknown  quantities.  This 
is  due  to  the  fact  that  not  all  the  equations  are  independent. 


FIRST  APPROXIMATION  383 

This  may  be  shown  if  we  add  together  all  the  equations  of  the 
fourth  set,  and  substitute  in  the  numerators  of  the  fractions 
thus  obtained  their  value  as  obtained  from  the  third  set, 
namely,  zero.  We  shall  then  evidently  obtain  the  first  equa- 
tion of  the  third  set.  Consequently  we  may  omit  any  one  of 
the  equations  of  the  third  and  fourth  sets.  There  will  then 
remain  just  as  many  equations  as  unknown  quantities,  and 
our  problem  is  exactly  determined. 

In  the  preceding  analysis,  we  have  throughout  assumed  a 
rate  of  interest  between  two  points  of  time  a  year  apart.  A  more 
minute  analysis  would  involve  a  greater  subdivision  of  the 
income-stream,  and  the  employment  of  a  rate  of  interest  be- 
tween every  two  successive  elements.  This  will  evidently 
occasion  no  difficulty  except  to  increase  the  number  of  equa- 
tions and  unknowns. 

§  5 

The  elaborate  system  of  equations  which  is  involved  when  m 
years  instead  of  two  years  are  considered  introduces  very  few 
features  of  the  problem  not  already  contained  in  the  simpler 
set  of  equations  first  given.  The  new  feature  of  chief  impor- 
tance is  that,  instead  of  only  one  rate  of  interest  to  be  deter- 
mined, there  are  now  a  large  number  of  rates.  It  is  too  often 
assumed,  in  theories  of  interest,  that  the  problem  is  to  deter- 
mine "  the  "  rate  of  interest,  as  though  one  rate  would  hold  true 
for  all  time.  But  in  the  preceding  equations  we  have  m— 1  sepa- 
rate magnitudes,  i\  i",  i'",  ...  i("»-i>.  Is  there  any  tendency  at 
work  to  make  these  rates  of  interest  equal  ?  Is  the  rate  of  in- 
terest which  expresses  the  ratio  of  exchange  between  this  year's 
and  next  year's  income  normally  equal  to,  or  nearly  equal  to,  the 
rate  of  interest  which  expresses  the  ratio  of  exchange  between 
next  year's  income  and  the  year  after  ?  Bohm-Bawerk '  put 
this  question,  and  answered  it  affirmatively,  stating  that  a 
species  of  arbitrage  transactions  tended  to  produce  this  result. 
If,  however,  we  examine  his  reasoning  closely,  we  shall  see  that 
the  only  proposition  he  has  proved  is  that,  if  the  rate  of  inter- 
est expressing  the  premium  on  the  goods  of  1888  as  compared 
with  1889  is  equal  to  the  premium  of  1889  over  1890,  then  a 
contract  for  the  exchange  of  the  goods  of  1888  for  those  of  1890 
will  take  place  at  this  same  rate.     But  what  is  really  needed 

1  Positive  Theory  of  Capital,  p.  280. 


384  APPENDIX   TO  CHAPTER  VII 

is  to  know  whether  (as  Bohm-Bawerk  assumes)  the  rate  of 
interest  connecting  the  years  1888  and  1889  is  the  same  as 
the  rate  of  interest  connecting  the  years  1889  and  1890,  and 
if  so,  why? 

Under  the  hypothesis  of  a  rigid  allotment  of  future  income 
among  different  time  intervals,  there  is  nothing  to  prevent  great 
differences  in  the  rate  of  interest  from  year  to  year,  even  when 
all  factors  in  the  case  are  foreknown.  This  is  clear  from  the 
fact  that,  by  a  suitable  distribution  of  the  values  of  Cj,  c,,  etc, 
there  may  be  produced  any  differences  in  the  values  of  i',  i",  i'", 
etc.  If  the  total  enjoyable  income  of  society  should  be  fore- 
known to  be,  in  the  ensuing  year,  10  billion  dollars,  in  the  fol- 
lowing year  one  billion,  and  in  the  third  year  20  billion,  and 
there  were  no  way  of  avoiding  these  enormous  disparities,  it 
is  very  evident  that  the  income  of  the  middle  year  would  have 
a  very  high  valuation  compared  with  either  of  its  neighbors, 
and  therefore  that  the  rate  of  interest  connecting  that  middle 
year  with  the  first  year  would  be  very  low,  whereas  that  con- 
necting it  with  the  third  year  would  be  very  high.  It  might 
be  that  the  members  of  such  a  community  would  be  willing  to 
exchange  $100  of  their  plentiful  10  billions  for  the  first  year, 
for  only  $101  out  of  their  scarce  one  billion  of  next  year,  but 
would  be  glad  to  give,  out  of  the  third  year's  still  more  plenti- 
ful 20  billions,  $150  for  the  sake  of  $100  in  the  middle  and 
lean  year.  The  reason  that,  in  actual  fact,  such  abrupt  and 
large  variations  in  the  rate  of  interest  as  from  1%  to  50%  are 
not  more  frequently  encountered  is  that  the  supposed  sudden 
and  abrupt  changes  in  the  income-stream  seldom  occur.  The 
causes  which  prevent  their  occurrence  are :  — 

(1)  The  fact  that  history  is  constantly  repeating  itself. 
For  instance,  there  is  regularity  in  the  population,  so  that  at 
any  point  of  time  the  outlook  toward  the  next  year  is  very 
similar  to  what  it  was  at  any  other  point  of  time.  The  indi- 
vidual may  grow  old,  but  the  population  does  not.  As  indi- 
viduals are  hurried  across  the  stage  of  life,  their  places  are 
constantly  taken  by  others,  so  that,  whatever  the  tendency  in 
the  individual  life  to  make  the  rates  of  preference  go  up  or 
down,  it  will  not  be  cumulative  in  society.  Relatively  speak- 
ing, society  stands  still. 

Again,  the  processes  of  nature  recur  in  almost  ceaseless 
regularity.     Crops  repeat  themselves  in  a  yearly  cycle.     Even 


FIRST  APPROXIMATION  385 

when  there  are  large  fluctuations  in  crops,  they  are  seldom 

world-wide,  and  a  shortage  in  the  Mississippi  valley  may  be 

compensated  for  by  an  unusually  abundant  crop  in  Russia  or 

Asia.     The   resultant  regularity  of   events   is  thus  sufficient 

to  maintain  a  fair  uniformity  in  the  income-stream  for  society 

as  a  whole. 

(2)  The  fact  that  the  income-stream  is  not  fixed,  but  may 

be   modified   in   other  ways   than  by  borrowing  and  lending. 

The  nature  of  these  modifications  are  considered  in  Chapter 

VIII. 

§6 

Let  us  now  return,  for  fuller  discussion,  to  the  second  con- 
dition, that  the  rates  of  preference  of  the  different  individuals 
are  equal  to  each  other  and  to  the  rate  of  interest. 

It  was  shown  in  Chapter  VII  that  when  the  individual  de- 
termined his  income  stream  so  that  his  marginal  rate  of  pref- 
erence for  present  over  future  income  was  equal  to  the  rate  of 
interest,  he  thereby  maximized  his  present  "  total  desirability." 
The  two  statements,  that  his  preference  rate  is  equal  to  the 
interest  rate,  and  that  his  "  total  desirability  "  is  a  maximum, 
are  thus  interequivalent,  and  either  may  be  deduced  from  the 
other.  Mathematically  this  may  be  shown  either  by  geometry 
or  by  algebra.     We  shall  begin  with  the  algebraic  method. 

Assume  at  first  that  only  two  years  are  considered.  The 
fact  that  total  desirability  depends  on  the  amount  of  income 
this  year  and  next  year  may  be  represented  by  the  equation 

where  U  represents  total  desirability  or  utility  of  an  individ- 
ual, and  the  equation  represents  this  t7  as  a  "  function "  of 
his  income-stream  consisting  of  c'  -f-  x'  this  year  and  c"  -1-  x" 
next  year.  As  we  shall  here  consider  only  one  individual,  we 
omit  the  subscript  numbers,  1,  2,  etc.,  previously  used  to  dis- 
tinguish different  individuals.  The  individual  will  attempt  to 
adjust  x'  and  x"  so  as  to  maximize  TJ.  By  the  theory  of  dif- 
ferential equations,  the  condition  that  U  shall  be  a  maximum, 
is  that  the  "  total  differential"  of  U  or  of  its  equal  F{c'  -\-  x\ 
c"  -+-  tc")  shall  be  zero,  thus 


8x'  8x' 

2c 


386  APPENDIX   TO  CHAPTER  VII 

where  the  8's  represent  the  "  partial  differentials  "  with  respect 
to  «'  and  x",  and  the  blank  parentheses  stand  for 

(c'+a;",  c"+a;"). 

From  this  equation  it  follows  that 

dx'         8x'    I     8x" 

The   ?e/?-hand  member  is  1  + 1,  as  may  be  seen  by  differen- 
tiating the  equation  of  the  loan  as  originally  stated,  viz. : 


a;"                                                                          da;" 
=  0.     This  differentiation  yields — 

1  +  i  ^  dx' 


The  right-\idindi  member,  being  the  ratio  of  this  year's  marginal 
desirability  to  next  year's  marginal  desirability,  is  by  defini- 
tion equal  to  1  +/.  Substituting  the  new  value  for  the  right 
and  left  members,  we  have 

whence  it  follows  that  i  =/. 

The  same  reasoning,  applied  to  three  or  more  years,  may 
now  be  expressed.  The  total  desirability  for  any  individual 
is  a  function  of  the  total  future  income-stream.  In  other 
words, 

U=F{c'  +  x',  c"  +  x",  c'"  +  x'",  etc.). 

The  individual  tries  to  make  this  magnitude  a  maximum.  In 
terms  of  the  calculus,  this  is  equivalent  to  making  the  first 
total  differential  equal  to  zero,  namely, 

,U=  i|^...  +  «|^.."  +  §£P..'"  +  etc.  =  0. 

This  total  differential  equation  is  equivalent  to  a  number  of 
subsidiary  equations  obtained  by  making  particular  suppositions 
as  to  the  different  variations.  Let  us,  for  instance,  suppose 
that  only  x'  and  x"  vary  in  relation  to  each  other  and  that  x'", 
x'"',  etc.,  do  not  vary.  Then  in  the  above  equation  all  terms 
after  the  second  disappear  and  the  equation  reduces  to 

_dx"     SF(  )    /8F(  ) 
dx'  ~    8x'    /     8  x" 

In  other  words,  1  +  <'  =  1  +/',  and  therefore  i'  =f. 


FIRST  APPROXIMATION 


387 


This  expresses  the  relation  between  the  first  and  second 
years.  If  we  wish  in  like  manner  to  express  the  corresponding 
connection  between  the  second  and  third  years,  let  us  assume 
that  x'  is  constant  and  x'",  etc.,  constant.  Then  the  first  term 
of  the  equation  disappears  and  all  after  the  third  term,  and 
the  equation  reduces  to 

_dx"'      8F(  )    /8F(  ) 
dx"  ~    8x"    /    8x"'   ' 

In  other  words,  1  +  i"  =  1  +/",  or  i"  =f" ;  and  so  on  for  each 
succeeding  year.  We  therefore  see  in  mathematical  language 
that  the  point  of  maximum  desirability  is  also  the  point  at 
which  the  marginal  rate  of  preference  for  each  year's  income 
over  the  next  year's  income  is  equal  to  the  rate  of  interest 
connecting  these  two  years. 

§  7 
We  turn  now  to  the  geometrical  interpretation.     In  Figure 
26,  let  the  point  P  be  found  such  that  its  coordinates  are  ci' 


-"    1020304050  60  70^ 


Fi(i.  2(1 . 


and  Ci",  the  values  of  this  year's  income  and  next  year's  in- 
come respectively,  c^  being  laid  off  along  the  horizontal  axis 


388  APPENDIX  TO  CHAPTER  VII 

OX^,  and  Ci"  being  laid  off  vertically.  In  the  same  way  any 
other  income-stream  may  be  represented  by  another  point,  the 
coordinates  of  which  represent  the  values  of  this  year's  and 
next  year's  income  respectively.  By  borrowing  or  lending, 
the  income-stream  P  is  changed  to  another  point  Q  to  be 
determined.  We  shall  assume,  as  before,  that  the  modifica- 
tion of  this  income-stream,  c/,  Cj",  through  borrowing  and 
lending  or  buying  and  selling  applies  only  to  the  first  and 
second  years ;  all  subsequent  years  are  therefore  omitted 
from  our  calcidations.  The  income-stream  that  is  the  com- 
bination of  the  two  magnitudes  Cj',  cJ',  —  the  fixed  income 
with  which  the  individual  is  supposed  to  be  endowed,  —  is 
represented  by  the  point  P.  But  this  income-stream,  c/,  c/',  he 
modifies  by  adding  algebraically  x^',  through  borrowing  (or  lend- 
ing, if  Xi  has  a  negative  value)  this  year,  and  adding  next  year, 
when  the  loan  is  paid,  the  sum  Xi",  which  is  equal  to  x^'  put  at 
interest,  but  of  opposite  sign ;  in  ot  herwords,  x^"  =  —  x'  (1  +  0 

X  " 
or  x/  -|-   '  '   .  =  0.     It  is  first  proposed  to  determine  x/  and  x^", 
1  4"  i 

assuming  that  the  rate  of  interest  is  a  fixed  and  given  magni- 
tude. The  new  income-stream,  c'  +  x',  c"  +  x",  will  be  repre- 
sented by  a  new  point,  Q,  different  from  P. 

To  find  this  point,  Q,  draw  the  line  AB  through  the^  point  P 
at  a  slope  determined  by  the  given  rate  of  interest,  namely,  so 

OTi 
that  yr—.  =1  +  1.     Then  the  new  point  will  lie  somewhere  upon 

this  straight  line.  For  (1)  the  present  value  of  the  modified 
income-stream  c/  +  x/,  c^"  +  x^"  is  the  same  as  that  of  the 
original  income-stream  c/,  c/' ;  and  (2)  the  straight  line  AB  is 
the  "  locus  "  or  assemblage  of  all  points  the  present  values  of 
the  income-streams  represented  by  which  are  the  same  as  the 
present  value  of  the  income-stream  represented  by  the  point  P 
through  which  AB  is  drawn. 

That  (1)  the  present  values  of  the  original  and  the  modified 
income-streams  are  the  same  is  due  to  the  fact  that  the  loan 
Xi  and  its  repayment  Xi"  are  equivalent  in  present  value.  This 
may  be  seen  by  transforming  the  formula  for  the  present 
value  of  the  modified  income-stream,  as  follows:  — 

^  II  _i_  ^  n  f,  II  /  >r  "    \  r  " 


FIRST  APPROXIMATION  389 

since  the  magnitude  in   parenthesis   is   zero   by  the   original 

hypothesis  as  to  a;/  and  Xi". 

That   (2)   the   line  AB  locates  all  points  of  present  value 

c "    . 
Ci  4-     ^ .  is  evident  from  analytical  geometry,  and  may  be 

shown,  among  other  ways,  as  follows :  — 

The  present  value  of  the  original  income-stream  c/,  q"  is 
equal  to  the  length  OA.     For 

OA=OC+CA 

c  " 


-1    -TT-— .J 


C." 


for  OC—Ci  by  construction  and  CA  =  —^—  by  the  similar  tri- 

l  +  ^• 

c "       OR 
angles  -4 CP  and  AOB,  whose  proportional  sides  give  — ^  =  -:— - 

^    ^  ""       CA      OA 


=  1  +  ?,  or  CA=^ 


c'' 


Similar  reasoning  applied  to  any  other  point  on  the  line 
AB  will  show,  in  like  manner,  that  the  present  value  of  the 
income  represented  by  that  point  is  also  OA.  Hence  every 
point  on  the  straight  line  jiB  represents  an  income-combination 
or  income-stream  having  the  same  present  value,  OA,  as  that 
of  the  income-stream  c',  c"  represented  by  P.  Similar  reason- 
ing shows  that  no  point  out  of  AB  represents  an  income-stream 
of  this  present  value.  Therefore  the  individual  who  is  pos- 
sessed of  the  income-stream  represented  by  P,  and  who 
modifies  this  income-stream  by  borrowing  and  lending,  merely 
shifts  the  point  representing  his  income-stream  alojig  the  line 
AB,  as  from  P  to  Q.  Which  of  all  the  points  on  this  line 
open  to  his  choice  will  he  select  ?  Evidently  he  will  select 
that  one  which  will  give,  for  him,  the  maximum  present  de- 
sirability. In  order  to  determine  this  point,  let  us  suppose 
that  the  desirability  corresponding  to  every  point  upon  the 
plane  is  indicated  by  a  number  attached,  and  that  through 
the  points  which  have  equal  desirability,  lines  of  equal  de- 
sirability, like  isothermal  lines  on  a  weather  map,  are  drawn.^ 
These  may  be  called  iso-desirability  lines.     If  any  two  points 

1  Cf.  the  writer's  "  Mathematical  Investigations  in  the  Theory  of  Value 
and  Prices,"  Fart  II,  Traiusactions  of  Conn.  Academy,  New  Haven,  1902, 
p.  68. 


390  APPENDIX  TO  CHAPTER  VII 

on  one  and  the  same  iso-desirability  curve  be  compared,  it  will 
be  seen  that  one  of  them  represents  an  income  richer  this  year 
and  poorer  next  year  than  the  income  represented  by  the 
other;  the  superiority  of  the  former  income  over  the  latter 
this  year  exactly  compensates  for  its  inferiority  next  year,  so 
that,  all  considered,  the  two  incomes  are  equally  desirable. 
It  is  clear  that  these  iso-desirability  lines  will  constitute  a 
"  family  "  of  curves,  each  approaching  the  axes  OX'  and  OX", 
and  that  the  numbers  attached  increase  in  magnitude  as  the 
curves  recede  from  the  origin  0.  The  curve  drawn  nearest 
the  axes  is  labeled  "  10 "  at  each  end,  to  signify  that  all 
points  upon  that  curve  have  a  desirability  to  the  individual 
represented  by  10.  The  point  P  evidently  has  a  desirability 
between  10  and  20.  As  we  proceed  from  P  toward  B  along 
the  line  AB,  it  is  evident  that  the  desirability  first  increases 
and  then  decreases,  reaching  the  maximum  at  Q,  where  the  line 
AB  is  tangent  to  one  of  the  family  of  curves.  This  point  Q  is 
therefore  the  point  sought,  and  represents  the  income-combina- 
tion which  has  the  maximum  present  desirability.  Thus,  for 
the  individual,  the  solution  of  the  problem  of  how  much  to 
borrow  or  lend  is  determined  geometrically  by  drawing  through 
the  point  P,  representing  his  fixed  original  income-endowment, 

a  straight  line  at  the  slope  — -  =  1  +  i',  and  finding  the  point 

OA 

Q  upon  this  line  at  which  it  is  tangent  to  some  one  of  the  num- 
berless curves  of  equal  desirability.  Q  differs  from  P  in 
having  one  of  its  coordinates  larger  (by  x-^")  and  the  other 
smaller  (by  —Xi). 

The  fact  that  the  iso-desirability  curves  at  the  right  slope 
less  than  45°  interprets  the  fact,  which  should  not  be  lost  sight 
of,  that  if  this  year's  income  is  sufficiently  abundant  or  next 
year's  income  sufficiently  scarce,  or  both,  that  this  year's 
goods  may  exchange  for  next  year's  on  less  than  even  terms  j 
that  is,  that  the  rate  of  time-preference  may  be  negative. 

§  8 
Not  only  is  it  true  that  Q  represents  the  point  of  maximum 
desirability,  but  also  that  at  the  point  Q  the  rate  of  preference 
/i  is  equal  to  the  rate  of  interest.  First  we  observe  that  the 
rate  of  preference  for  present  over  future  income  at  any  point 
depends   upon   the   slope  of  the  iso-desirability  curve  which 


FIRST  APPROXIMATION  391 

passes  througli  that  point.  To  make  this  clear,  let  us  consider, 
on  any  of  the  iso-desirability  curves,  svich  as  70-70,  the  point 
M  and  an  adjacent  point  N.  The  substitution  of  the  income- 
combination  represented  by  N  for  that  represented  by  M  in- 
volves the  sacrifice  of  an  amount  of  this  year's  income  repre- 
sented by  MS,  which  may  be  called  —  A  x',  for  the  sake  of  an 
addition  to  next  year's  income  represented  by  NS,  or  Ace". 
If  the  points  M  and  N  are  indefinitely  near  together,  we 
may  represent  MS  by  —dx',  and  ^^S"  by  dx".  The  loss  in 
desirability  by  surrendering  MS  is  represented  by  the 
difference  in  number  between  the  iso-desirability  curves 
through  M  and  *S,  namely,  70  —  60,  or  10.  Likewise,  the  gain 
in  desirability  by  the  addition  of  SN  to  next  year's  in- 
come is  represented  by  the  difference  between  the  numbers 
corresponding  to  iso-desirability  curves  through  S  and  N, 
also  70  —  60,  or  10.  In  other  words,  the  loss  in  desirability 
through  the  surrender  of  MS  is  equal  to  the  gain  in  desira- 
bility through  the  addition  of  SN,  or,  the  desirability  of  the 
loss  of  MS  of  this  year's  income  equals  the  desirability  of  the 
gain  of  NS  of  next  year's  income.  Since,  therefore,  SM  and 
SN,  or  —  Ax'  and  Aic",  are  the  amounts  of  income  for  the  two 
respective  years  which  possess  equal  desirability,  it  is  evident 
that  the  degree  of  desirability  ;9e?'  xmit  of  income  for  this  year 
and  next  year  will  be  in  the  inverse  proportion.  Thus,  if  SM 
is  two  hundred  and  SN  is  three  hundred  dollars'  worth  of  in- 
come, this  means  that,  for  the  particular  individvial  for  whom 
the  figure  is  drawn,  having  an  income-stream  represented  by 
the  point  M,  $200  taken  from  this  year's  income  would  be 
exactly  compensated  for  in  present  estimation  by  the  addition 
of  $300  to  next  year's  income.  Hence  the  desirability  per 
dollar  of  the  present  income  is  14-  times  the  desirability  per 
dollar  of  next  year's  income. 

Symbolically  these  relations  are :  — 

Desirability  of  A  a;'  +  desirability  of  A  x"     =0. 

_    desir.  Aa;'        ,     desir.  Aa^'V     ,,  ^ 

Or  — — -;—  A  x'  + -^r-  ^  ^  =^» 

A  x'  Ax" 

or  -—I  Ax' +  -—7,  Ax"  =0, 


Ax'  'Ax' 

A   "  '  x'Ax 


^     ^  ^^*  »  (»  A  f  T4TCT         Tiro 

or     -7—77  :  —. —  =  Ax":  —  A  x'  =  NS :  MS 


392  APPENDIX  TO  CHAPTER  VII 

That  is,  the  desirability  of  an  additional  present  dollar  is 
to  that  of  an  additional  dollar  next  year,  as  NS  to  3IS,  or  the 
slope  of  the  line  joining  M  and  iV.  If  the  points  3/ and  Nave 
indefinitely  near  together,  the  slope  will  be  the  slope  of  the 
iso-desirability  curve  through  M.  Thus  the  sloj)e  of  any  of 
the  curves  in  the  diagram  at  any  point  is  the  geometrical  rep- 
resentation of  the  relative  valuation  of  present  and  future 
income  which  the  individual  feels  when  in  possession  of  the 
income-stream  represented  by  that  point.  We  have  already 
specified  that  the  slope  of  the  straight  line  AB  represents  the 
ratio  of  exchange  of  this  and  next  year's  income.  Thus  the 
slope  of  the  curves  represents  the  subjective,  and  the  slope  of 
the  line  the  objective,  ratio  of  equivalence  for  the  two  years. 
The  former  slope,  the  ratio  of  the  marginal  desirability  of  this 
year's  income  to  the  marginal  desirability  of  next  year's  income, 
is,  by  our  previous  definition,  1  -f /j,  just  as  the  latter  slope  is 
l  +  i. 

Applying  these  ideas  to  the  particular  point  Q,  it  is  clear  that 
the  slope  of  the  iso-desirability  curve  through  Q  is  equal  to  the 
slope  of  the  straight  line  BA.  But  the  slope  of  the  desirability 
curve  is  1  -f /i,  and  the  slope  of  the  straight  line  AB  is  1  -f  /, 
therefore,  for  any  individual, 

1  +/i  =  1  +  i, 
or  J\  =  i. 

Hence  the  individual  who  modifies  his  income  from  P  by  a 
loan  at  the  rate  i  will  shift  it  to  a  point  Q,  such  that  his  sub- 
jective rate  of  preference /^  which  corresponds  to  that  point  will 
be  equal  to  the  objective  rate  of  interest  /,  —  or,  speaking  geo- 
metrically, so  that  the  ''slope"  of  his  curves  will  be  made 
equal  to  the  "slope"  of  the  market. 

We  have  presented  the  geometrical  method  in  considerable 
detail,  in  the  belief  that  it  is  well  worth  mastering.  It  will 
be  found  especially  helpful  when  extended  so  as  to  apply  to 
the  more  complicated  problem  discussed  in  the  Appendix  to 
Chapter  VIII. 

§9 

If  we  proceed  from  the  consideration  of  two  years  to  that  of 
three,  we  may  still  represent  our  problem  geometrically  by 
using  three  dimensions.  Let  us  consider  three  mutually  per- 
pendicular axes  OX',  OX",  OX'",  and  represent  the  income- 


FIRST  APPROXIMATION  393 

combination  or  income-stream  for  the  particular  individual  by 
the  point  P,  whose  coordinates  c',  c",  and  c'"  are  the  three 
years'  income-installments  with  which  the  individual  is  initially 
endowed.  Then  through  the  point  P  draw,  instead  of  the 
straight  line  in  the  previous  representation,  a  j)lane  ABC  cut- 
ting the  three  axes  in  A,  B,  and  C.     This  plane  has  a  slope 

with  reference  to  the  two  axes  OX'  and  OX"  of  -— -  equal  to 

OA 

1  +  i',  and  has  a  slope  with  reference  to  the  axes   OX"  and 

OG 
OX'"  represented  by ——  equal   to   l-J-i".     The  letters  t'  and 

V  here  represent,  as  before,  the  rate  of  interest  in  the  ex- 
change of  this  and  next  year's  goods,  and  of  next  year's  and 
the  year  after.  Now  suppose  the  space  between  the  axes  to 
be  filled  with  iso-desirability  curved  surfaces  like  the  coats  of 
an  onion,  such  that  for  all  points  on  the  same  surface  the  total 
desirability  of  the  income-stream  represented  by  those  points 
will  be  the  same.  These  surfaces  will  be  such  as  to  approach 
the  three  axes  and  the  planes  between  them,  and  also  such  that 
the  attached  numbers  representing  their  respective  total  desira- 
bilities shall  increase  as  they  recede  from  the  origin  O.  The 
plane  ABC  drawn  through  P  at  the  slope  fixed  by  the  rates  of 
interest,  as  just  indicated,  will  now  be  tangent  to  some  one  of 
the  iso-desirability  surfaces  at  a  point  Q,  which  is  the  point  at 
which  the  individual  will  fix  his  income.  For  every  point  on 
the  plane  ABCvi'iW  have  the  same  present  value,  and  every  point 
on  this  plane  is  available  to  him  by  borrowing  and  lending  (or 
buying  and  selling)  at  the  rates  /'  and  i",  but  not  all  of  them 
will  have  the  same  desirability.  He  will  select  that  one  which 
has  the  maximum  desirability,  and  this  will  evidently  be  the 
point  Q,  at  which  the  plane  is  tangent  to  one  of  the  family  of 
iso-desirability  surfaces.  Reasoning  similar  to  that  given  for 
two  dimensions  will  show  that  this  point  will  be  such  that 
//  =  t'and//'  =  t". 

To  proceed  beyond  three  years  would  take  us  beyond  the 
limitations  of  space;  for  we  should  then  need  in  our  represen- 
tation more  than  three  dimensions.  Such  a  representation  is 
of  little  meaning  except  to  mathematicians,  since  it  cannot  be 
fully  visualized.  For  the  practical  purpose  of  visualization, 
the  simple  geometrical  representation  in  two  dimensions, 
though  limited  to  two  years,  is  the  most  helpful. 


394  APPENDIX  TO  CHAPTER  VII 

§10 

Having  shown  the  geometrical  representation  as  applied  to  a 
particular  individual,  we  now  proceed  to  show  how  the  rate  of 
preference  is  determined  for  a  series  of  individuals.  To  recur 
to  the  geometrical  representation  in  Fig.  26,  where  only  two 
variables  are  considered,  the  problem  is  as  follows :  — 

Given  a  number  of  different  individuals,  each  with  his  own 
separate  point  P  and  his  own  separate  set  of  iso-desirability 
curves,  we  are  required  to  draw  through  these  points  straight 
lines  parallel  to  each  other  at  such  a  slope  as  to  "clear  the 
market,"  in  other  words,  such  that  the  sum  of  the  x'^s  for  the 
different  individuals  shall  be  zero,  and,  as  implied  thereby, 
that  the  sum  of  the  a;"'s  shall  also  be  zero. 

It  is  evident  that,  according  as  the  slope  of  the  lines  AB 
changes,  the  points  of  tangency,  the  Q's,  for  the  different  indi- 
viduals will  vary,  which  means  that  the  amount  borrowed  or 
lent,  namely,  x'  and  x",  will  change.  We  have  then  a  swarm  or 
group  of  fixed  points,  the  P's,  and  another  swarm  of  variable 
points  Q's.  By  rotating  the  lines  each  about  its  pivot  P,  and 
so  that  all  remain  parallel  to  each  other,  we  can  evidently  shift 
the  position  of  the  second  swarm  of  points,  the  Q's.  The  solu- 
tion is  found  by  fixing  upon  such  a  slope  of  the  lines  that  the 
center  of  gravity  of  the  Q  swarm  is  brought  into  coincidence 
with  the  fixed  center  of  gravity  of  the  P  swarm.  The  slope  of 
the  lines  AB  which  will  accomplish  this  result  is  the  rate  of 
interest  which  will  just  clear  the  market;  for  the  horizontal 
deviations,  Xi,  x^',  etc.,  between  the  P  and  Q  for  each  different 
individual  will  then  be  self-canceling,  their  algebraic  sum  being 
zero,  and  the  same  is  true  for  the  vertical  deviations  x^",  x^",  etc. 

For  three  dimensions,  we  have  precisely  similar  determina- 
tions. The  problem  of  the  rate  of  interest  is  here  solved  by 
finding  such  an  orientation  for  the  various  planes  through  the 
points  called  P's  as  will  bring  the  center  of  gravity  of  the 
tangential  points,  the  Q's,  into  coincidence  with  the  fixed  center 
of  gravity  of  the  P's. 


APPENDIX  TO  CHAPTER  VIII 

Second  Approximation 

(This  Appendix  should  be  read  as  a  whole  after  Chapter  VIII.) 

§1 

In  the  Appendix  to  Chapter  VII  we  found  that  the  number 
of  equations  available  for  determining  the  rate  of  interest  was 
equal  to  the  number  of  unknown  quantities,  and  therefore  that 
the  rate  of  interest  and  the  other  associated  variables  were 
determinate  under  the  assumption  there  made.  This  assump- 
tion was  that  all  income-streams  were  unalterable,  except  as 
they  could  be  modified  by  borrowing  and  lending,  or  buying 
and  selling.  We  now  introduce,  in  place  of  such  a  fixed  income- 
stream,  the  hypothesis  of  a  range  of  choice  between  different 
income-streams.  This,  however,  does  not  destroy  the  deter- 
minateness  of  the  interest  problem ;  for  along  with  the  new 
variables  introduced,  we  find  an  equal  number  of  new  equations. 

Let  us,  then,  state  and  count  the  equations  which,  under  our 
several  hypotheses,  determine  the  rate  of  interest.  The  in- 
come-stream, we  must  remember,  no  longer  consists  of  known 
and  fixed  elements,  c/,  c/',  c/",  etc.,  as  assumed  in  Chapter  VII, 
elements  which  can  be  modified  only  by  exchange;  it  now  con- 
sists of  unknown  and  variable  elements  which  we  shall  designate 
by  y\,  111",  yi",  etc.  This  elastic  income-stream  may  be  mod- 
ified in  two  ways :  by  the  variations  in  these  y's,  as  well  as  by 
the  method  which  we  found  applicable  for  rigid  income- 
streams,  namely,  the  method  of  exchange  —  borrowing  and 
lending  or  buying  and  selling.  The  alterations  effected  by  the 
latter  means  we  shall  designate  as  before  by  a.-/,  a\",  x^'",  etc., 
for  successive  years.  These  are  to  be  algebraically  added  to 
the  original  income-items  (the  y's),  deductions  being  included 
in  this  addition  by  assigning  negative  values.  The  income- 
stream  as  finally  determined  is  therefore  expressed  by  tlie 
installments,  ?/i'  -|-  x/,  y^"  +  a-/',  i//"  -|-  x,'",  etc. 

395 


396  APPENDIX   TO  CHAPTER  VIII 

One  of  the  determining  conditions  stated  in  Chapter  VII  is 
that  the  individual  rates  of  preference  are  functions  of  the  in- 
come-streams. Algebraically  stated,  this  condition  gives  the 
equations :  — 

/i-  =  Fy  (y,'  +  x,',y,"  +  X,",  •  •  •  y^  (->  +  a^<-')» 
/2-  =  F,-  (y,'  +  X,',  y,"  +  x,",'-  y^^^^  +  x,<% 

/„-  =  F„.(yJ  +  xj,  yj'  +  x„",  ...  yj-)  +  x„^'^>). 

These  equations  express  the  individual  rates  of  preference 
for  the  Jirst  year's  income  compared  with  the  next.  To  express 
the  preference  for  the  second  year's  income  compared  with  the 
next,  there  will  be  another  set  of  equations,  namely :  — 

/i-  =  ^1"  (yi"  +  <,  ih'"  +  ^r, '  •  •  yi'""'  +  x,^-^), 
j],.  =  F,..Q/j'+x^', yr^  +  x.^"^^), 

fn-  =  K..(yJ'  +  x„",  2/„^"'^  +  a.-„<'">). 

For  the  third  year,  as  compared  with  its  successor,  there 
would  be  another  similar  set,  with  " '"  "  in  place  of  "  "  ",  and 
so  on  to  the  next  to  the  last  or  (m  —  1)  year  as  compared  with 
the  last.  Since  each  of  these  m  —  1  groups  of  equations  con- 
tains n  separate  equations,  there  are  all  together  w  (m  —  1)  equa- 
tions in  the  entire  set. 

The  next  condition,  that  the  rates  of  preference  and  of  inter- 
est will  be  equal,  is  the  same  as  in  the  first  approximation,^ 
and  is  represented  bj'-  the  same  w(m— 1)  equations,  namely :  — 

i"=f,"        =/,"     = =/;/', 

^•(m-l)_  ^(m-I)  ...  _  ^(m-l)  _     =/'("'~^>. 

The  two  sets  of  equations  which  express  the  "  clearing  of  the 
market"  and  equivalence  of  loans  and  repayments  will  also 
be  the  same  as  before,  and  represented  by  the  same  m  equa- 
tions :  — 

Xr'  +x,'  +  ...  +x,:  =0, 

a,/'4.x,"-f-... +x„"  =  0, 

Xi^""^  +  x^^""^  +  •••  +  a-',/""  =0; 
1  See  Appendix  to  Ch.  VII,  §  4. 


SECOND  APPROXIMATION  397 

and  the  same  n  equations  : 

'     1  +  i'    (i+i')(i+i"y     "^  (i+i')(i+t")..(i+i(".))=o, 


!  +  *■'  (l  +  i')(l+t")..(l  +  i-)=0, 

a-n'  +  •••  =0. 

§2 

These  four  sets  of  equations  are  the  same  in  number  as 
the  corresponding  sets  given  in  the  Appendix  to  Chapter 
VII,  namely,  27nn  +  m  —  n,  or,  for  reasons  there  given,  only 
2mn  4-  m  —  w  —  1  mdependent  equations.  These  equations  dif- 
fer from  the  equations  of  the  preceding  Appendix  only  in  the 
first  set,  which  contain  ?/'s  in  place  of  c's.  The  c's  were  con- 
stants, but  the  2/'s  are  unknown  quantities.  Consequently, 
the  number  of  unknowns  is  greater  than  the  number  in  the 
first  approximation,  whereas  the  number  of  equations  thus  far 
expressed  is  the  same.  We  therefore  need  to  seek  for  new 
equations  to  supply  the  deficiency.  These  additional  equa- 
tions are  found  from  the  condition  that  the  choice  among  the 
optional  income-streams  will  fall  upon  that  one  which  possesses 
the  maximum  present  value. 

The  range  of  choice,  i.e.  the  complete  list  of  optional  income- 
streams,  will  include  many  which  are  ineligible.  By  an  ineli- 
gible income-stream  is  meant  one  which  would  not  be  selected 
whatever  might  be  the  rate  of  interest,  —  whether  zero  or  one 
million  per  cent.,  —  being  smaller  for  every  year  than  some 
other  stream  on  the  list.  Excluding  these  ineligibles,  the 
remaining  options  constitute  the  effective  range  of  choice.  This 
effective  range  of  choice  is  subject  to  the  "technical"  limita- 
tions of  productive  conditions,  and  constitutes  the  technical 
conditions  which  influence  the  rate  of  interest.  If  this  list  of 
options  be  assumed,  for  convenience  of  analysis,  to  consist  of 
an  infinite  number  of  options  varying  from  one  to  another,  not 
by  sudden  jumps,  but  continuously,  the  complete  list  can  be 
expressed  by  those  possible  values  of  ?/i',  ?/i",  ...  yi^™^  which 
will  satisfy  an  empirical  equation 

the  form  of  which  depends  on  the  particular  technical  condi- 
tions to  which  the  capital  of  individual  No.  1  is  subjected, 


398  APPENDIX  TO  CHAPTER  VIII 

whether  dependent  on  his  personal  characteristics  or  on  the 
physical  and  technical  conditions  of  his  business.  Thus  the 
form  of  the  function  <^i  will  be  one  thing  if  the  capital  of 
the  individual,  which  yields  the  y's,  consists  largely  of  mines 
which  are  failing,  and  quite  another  if  it  consists  of  forests 
recently  planted.  In  the  former  case,  the  equation  will  be 
satisfied  only  by  values  of  the  2/'s  such  that  the  earlier  y's  (as 
y'l  or  2/1")  are  comparatively  large  and  the  latter  y's  (as  y^""'^^  or 
t/*'"')are  comparatively  small ;  whereas  in  the  latter  case  the  series 
of  y's  must  conform  to  the  opposite  condition.  The  equation, 
therefore,  while  it  admits  of  an  infinite  number  of  arrays  of 
y's,  does  not  admit  of  their  variation  ad  libitum.  It  represents 
the  limitations  to  which  the  variation  of  the  income-stream 
must  conform.  Each  set  of  values  of  y^,  yi",  ...  yi^""^  which 
will  satisfy  this  equation  represents  an  optional  income-stream. 
Out  of  this  infinite  number  of  options,  that  particular  one  will 
be  selected  of  which  the  present  value  is  a  maximum. 

Now  the  present  value  Vi  of  any  income-stream  2/1',  yi",  ••• 
y/"*^,  of  individual  No.  1,  is  evidently 

The  condition  that  this  expression  shall  be  a  maximum  is  that 
the  first  differential  quotient  shall  be  zero.     That  is 

dV,  =  dy,'  +  3^,  +  (i^,.,;'i^,„)  +  etc.  =  0. 

This  last  equation  expresses  the  relations  which  must  exist 
between  dy^,  dy^',  dy^'",  etc.,  in  order  that  the  income-stream 
Vif  Vi")  yi"\  et-c-j  niay  have  the  maximum  present  value.  This 
condition  contains  within  itself  a  number  of  subsidiary  con- 
ditions. To  derive  these,  let  us  consider  a  slight  variation  in 
the  income-stream,  affecting  only  the  income-installments  of 
the  first  two  years,  t/j'  and  y^"  (the  remaining  installments, 
7/1'",  etc.,  being  regarded  as  invariable),  and  let  us  denote  the 
values  of  dyi,  dyi",  under  this  assumption  of  restricted  varia- 
tion, by  Sy/,  8yi".  Then,  remembering  that,  under  the  sup- 
posed condition,  dyi",  dyi'',  etc.,  will  be  zero,  the  above 
equation  becomes 


SECOND  APPROXIMATION  399 

from  which  it  is  evident  that 

But  the  left-hand  member  of  this  equation  is  evidently  the 
marginal  rate  of  return  on  sacrifice  as  between  next  year's 
income  and  this  year's  income,  or  the  ratio  of  the  increase 
which  may  be  effected  in  next  year's  income  by  a  given  sacri- 
fice in  this  year's  income.     If  we  call  the  jyremium  in  this 

ratio  of  return  r/,  we  may  express  —  -p-y  as  1  +  r/,  and  write 

the  above  equation  thus :  — 

l  +  r/  =  l  +  t', 
or  thus  :  —  ri'  =  i'. 

In  other  words,  the  condition  that  the  marginal  rate  of  return 
on  sacrifice  is  equal  to  the  rate  of  interest  follows  as  a  consequence 
of  the  general  condition  that  the  present  value  of  the  income- 
stream  must  be  a  maximum.  This  proposition  and  its  proof 
correspond  to  those  in  regard  to  desirability,  which  have 
already  been  discussed  in  Appendix  to  Chapter  VII,  §  6,  that 
the  condition  of  maximum  desirability  is  equivalent  to  the 
condition  that  the  marginal  rate  of  preference  is  equal  to  the 
rate  of  interest. 

The  same  reasoning  may  be  applied  to  successive  years. 
Thus,  if  we  assume  variations  in  y"  and  y'",  without  any  vari- 
ations in  the  other  elements  of  the  income-stream,  ?/',  y",  etc., 
the  original  differential  equation  becomes 


1+V  '    (l  +  i')(i4.|") 

or  1 -f- ri"  =  1 -f  i", 

or  r/'  =  i". 

Corresponding  analysis  applied  to  each  successive  year  will 
show  that  the  annual  successive  marginal  rates  of  return  on 
sacrifice  are  equal  to  the  annual  successive  rates  of  interest. 

All  this  reasoning  implies  that  there  is  a  possibility  of  con- 
tinuous variation,  and  that  at  the  margin  it  is  possible  to  make 
slight  variations  in  any  two  successive  years'  incomes  without 


400  APPENDIX  TO  CHAPTER  VIII 

disturbing  the  incomes  of  other  years.     The  values  of  1  +  r/, 

l-{-ri",etc.,OT—j-~,  —  ~jj-  (the  rate  at  which  the  second  year's 

income  may  be  increased  by  decreasing  the  first  year's  income, 
and  the  rate  at  which  the  third  year's  income  may  be  increased 
by  decreasing  the  second  year's  income,  etc.),  may  be  found  in 
terms  of  y/,  y/'  •••  y/'"^  by  differentiating  the  equation  for  the 
effective  range  of  choice,  <^i(?/i',  yi",  •••  ^//'"O  —^-  "^^^^  differ- 
entiation gives 

■ '   =^Ayi',yi",etc.), 


etc. 


■■^i"(Ui,  ?/i",etc.), 


Writing   together  the  equations  of  partial  differentiation,  we 
have,  as  our  new  set  of  equations :  — 

1  +  i'=  1  +  n'  =  .Ai-,  (y,',  y,",  etc.) 
=  1  +  7-2"=  i/'2"  (2/2',  2/2',  etc.) 

=  1  +  r„'  =  ./.„.  (yj,  y„",  etc.). 

These  equations,  2  n  in  number,  relate  to  the  rates  of  interest 
and  return-on-sacrifice  only  as  between  the  first  and  second 
years.  The  following  similar  2n  equations  relate  to  the  rates 
between  the  second  and  third  years :  — 

l  +  i"=l  +  r,"=^,.(y,",y,"',etc.) 
=  l+r,"=^i,.,.(y,",y,"',etG.), 
etc. 

Exactly  similar  equations  apply  to  each  year  as  related  to  its 
successor,  until  we  reach  the  final  set,  which  connects  the  next 
to  the  last  year  with  the  last,  viz.:  — 

I  _^  ^-Cm-l)  =  1  +  r/""-!)  =  ij/^On-l)  (3/1",  2/1'",   etc.). 

As  there  are  here  (m— 1)  sets  of  equations  and  2  n  in  each  set, 
the  total  number  of  equations  in  these  sets  is  2  n  (m  —  1).  These 
equations,  together  with  the  n  equations  of  effective  range  of 
choice  for  the  different  individuals,  viz.:  — 

<^i  (yi,  yi",  etc.)  =  0, 
<t>2  (2/2',  y-J',  etc.)  =  0, 

«^«  CVnS  2/.",  etc.)  =  0, 


SECOND  APPROXIMATION  401 

give  therefore  2  ?i(m—l)  +  n  or  2m7i—w,  the  total  number  of  new 
equations  in  addition  to  those  repeated  or  adapted  from  Appen- 
dix to  Chapter  VII.  The  number  of  independent  equations 
thus  repeated  or  adapted  from  the  previous  Appendix  was 
2  mn  +  m  —  H  —  1.     Hence  we  have :  — 

number  of  old  equations,    2  m»  +  m     —  n  —  1, 
+  number  of  new  equations,   2  mn  —  n, 

=  number  of  total  equations,  4  mn  +  m  —  2  n  —  1. 

Examination  will  show  that  the  number  of  unknowns  will 
also  be  4  mn  -\-m  —  2n  —  l.  For  all  of  the  2  mn  -\-  m  —  7i  —  l 
unknowns  previously  used  (in  Appendix  to  Chapter  VII)  are 
here  repeated,  and  in  addition,  the  new  unknowns,  the  y's  and 
the  r's,  are  introduced.  There  is  one  y  for  each  individual  for 
each  year,  the  total  array  being 

yi,  yi",  '  .  •  2//'"^ 


yJ,  2/n",  ■ . .  yn^""' 


The  number  of  these  y's  is  evidently  mn. 

There  is  one  r  for  each  individual  for  each  pair  of  succes- 
sive years,  i.e.  first  and  second,  second  and  third,  etc.,  and 
next  to  last  and  last,  the  total  array  being 

7-2',  r2",.-.r/"-i>, 


'    r   "   ...V  ("«-l) 


*•   '     7*    '      .  .  .  ■)• 


The  number  of  these  r's  is  evidently  n(7n  —  1). 

In  all,  then,  the  number  of  new  unknowns,  additional  to 
those  of  the  previous  Appendix,  is  mn  -f  w  (m  —  1)  or  2  mn—n. 
Hence  we  have : 

number  of  old  unknowns,    2  mn  -\-m    —  w  —  1, 
number  of  new  unknowns,   2  mn  —  n, 

total  number  of  unknowns,  4  mn  +  m  —  2n  —1, 

which  total  is  the  same  as  the  number  of  independent  equa- 
tions. Therefore  the  problem  of  the  rate  of  interest  and 
related  magnitudes  is  determinate  under  the  conditions  pre- 
scribed. 

The  complication  mentioned  in  Chapter  VIII,  §  14,  that  the 
2d 


402 


APPENDIX   TO  CHAPTER  VIII 


income-stream  itself  depends  npon  the  rate  of  interest,  does 
not  affect  the  determinateness  of  the  problem.  It  leaves  the 
number  of  equations  and  unknowns  unchanged,  but  merely 
introduces  the  rate  of  interest  into  the  set  of  equations  express- 
ing the  influence  of  the  technique  of  production.  These  now 
become 

<l>i(yi,  yi",  etc.,  i',  i",  etc.)  =  0, 

etc.,  and  their  derivatives,  the  kj/  functions,  are  likewise  altered. 


§3 

The  intricate  system  of  equations  just  stated  may  be  better 
understood  by  means  of  a  geometrical  representation. 

First  we  shall  represent  the  range  of  choice.  Let  us  suppose, 
for  simplicity,  that  only  two  years  need  to  be  considered,  so 


that  the  only  unknown  2/'s  or  income-installments  are  y'  and  y", 
all  the  y's  for  succeeding  years  being  regarded  as  fixed.  In 
other  words,  let  us  suppose  the  case  of  a  farmer  who  is  consid- 
ering the  choice  between  different  methods  of  cultivating  his 
farm  for  this  and  next  year,  but  does  not  take  into  considera- 


SECOND   APPROXIMATION  403 

tion  any  possible  variations  in  the  income  from  his  farm  for 
succeeding  years.  He  has  the  options  of  allowing  his  land  to 
lie  fallow  both  the  years ;  or  to  lie  fallow  the  first  year  and 
yield  an  income  the  second  year ;  or  to  yield  an  income  the  first 
year  and  lie  fallow  the  second ;  or  to  cost  him  a  net  loss  this 
year  in  order  to  add  to  the  income  next  year ;  or  to  yield  him 
something  both  years,  —  from  nothing  up  to  the  maximum  pos- 
sible, though  the  maximum  for  one  year  would  be  incompatible 
with  the  maximum  for  the  other.  The  farmer  has  here  a 
choice  among  an  indefinite  number  of  income-streams. 

Let  us  in  Fig.  27  measure  ?/'  along  the  axis  OT^,  and  y" 
along  the  axis  OY".  Then  the  point  j9  has  for  its  coordinates 
y'  and  y",  that  is,  for  its  abscissa  Oc  =  y',  and  for  its  ordinate, 
cp  =  y".  This  point  thus  represents  one  of  the  optional  income- 
streams.  In  like  manner  we  may  represent  all  other  options 
by  a  series  of  other  points,  as  shown  by  the  dots  in  the  diagram. 
Out  of  this  swarm  of  points,  each  representing  a  particular  option, 
only  one  will  of  course  be  chosen.  The  point  to  be  selected  will, 
as  we  know,  be  that  which  corresponds  to  the  maximum  pres- 
ent value.  To  find  it  we  do  not  need  to  consider  all  the  points 
in  the  entire  swarm,  for  some  of  them  are  evidently  out  of 
the  question.  Thus,  if  through  the  point  p  we  draw  the  line 
Op  and  prolong  it  to  p',  it  is  evident  that  the  combination 
or  option  represented  by  the  point  p'  will  have  a  higher 
present  value  than  that  represented  by  p,  no  matter  what  the 
rate  of  interest  may  be ;  for  p'  evidently  has  both  of  its  co- 
ordinates y'  and  y"  larger  than  the  coordinates  of  p.  In 
other  words,  p'  represents  an  income-stream  which  is  larger 
than  j»  both  this  year  and  next  year,  and  must  consequently 
have  a  larger  present  value,  whether  the  rate  of  interest  be 
1  %  or  100%.  Consequently,  of  all  the  points  along  the  line 
Op  we  may  disregard  all  except  the  one  point  (p')  remotest  from 
the  origin  0,  or  on  the  boundary  of  the  entire  mass  of  points. 
In  like  manner,  by  drawing  other  lines  from  0  we  may  see 
that  the  only  points  which  need  to  be  considered  are  the 
points  lying  on  the  boundary  p'tii  of  the  entire  mass  of 
points.  These  are,  so  to  speak,  the  only  eligible  points. 
Among  them,  the  one  which  represents  the  final  choice  will 
differ  according  to  the  rate  of  interest ;  but  whatever  the  rate 
of  interest,  the  choice  will  always  fall  on  a  point  in  the  desig- 
nated perimeter.  Therefore  the  perimeter  j)'tli,  etc.,  the  boun- 
dary of  the  swarm,  alone  represents  the  effective  range  of  choice. 


404  APPENDIX   TO  CHAPTER  VIII 

The  effective  range  of  choice  includes  only  the  convex  por- 
tions of  the  boundary,  the  portions  which  would  be  points  of 
tangency  ^  of  a  straight  line  such  as  ah,  touching  and  not  cut- 
ting the  boundary,  and  revolving  about  the  boundary  as  an 
"envelope."  We  may  still  further  restrict  the  portions  of  the 
boundary  to  be  included  by  limiting  the  position  of  the  revolv- 
ing line  ah  to  the  vertical  position  at  the  right  and  to  the  45" 
position  at  the  left.  Any  further  rotation  to  the  left  would 
imply  a  negative  rate  of  interest,  which  need  not  be  considered. 

The  configuration  of  this  boundary  line  is  the  geometrical 
representation  of  those  technical  conditions  which  limit  the 
income-stream  available  from  capital.  This  boundary  line 
representing  the  effective  range  of  choice  will  be  quite  different 
for  different  times  and  places.  It  will  be  different  according 
to  whether  the  capital  of  the  individual  considered  consists 
largely  of  land,  of  machinery,  or  of  other  forms  of  wealth. 
It  is  at  this  point,  then,  that  the  technical  conditions  of  in- 
dustry enter  into  our  problem,  and  show  their  influence  upon 
the  rate  of  interest. 

In  order  to  find  what  point  on  the  boundary  will  be  selected 
as  the  final  choice,  let  us  draw  the  line  AB  such  that  all  points 
upon  it  will  represent  options  possessing  a  fixed  present  value 
OA,  AB  will  then  be  a  straight  line  of  which  the  slope  is  1  -f-  i ', 
depending  on  the  rate  of  interest.^  We  know  that  the  present 
value  of  the  income-stream  represented  by  the  point  p  is  given 
by  the  formula 

V=  y'  -f  T^ — 7,  +  constant  terms, 
1  -f- 1 

in  which  equation,  as  in  those  which  follow,  the  subscripts  "i", 
etc.,  are  omitted  for  convenience,  as  it  will  readily  be  remem- 
bered that  the  equations  and  diagrams  always  refer  to  a  particu- 
lar individual.  The  constant  terms  represent  the  discounted 
income  of  the  years  beyond  the  second  year,  the  income-install- 
ments of  which  are  by  hypothesis  fixed.  If  now  we  give  to  V 
a  fixed  value,  and   transpose   to   the  left-hand    member   the 

1  It  may  be  worth  observing  that,  of  its  intercepts  OA  and  OB,  OA  ia 
equal  to  the  value  of  the  income -stream  j/i',  j/i",  as  reckoned  by  discount 
in  advance,  and  OB  is  equal  to  that  value  multiplied  by  the  factor  l-f-t'. 
Hence  OB  is  the  value  of  the  same  income-stream  reckoned  by  accumula- 
tion next  year.  See  The  Nature  of  Capital  and  Income,  Appendix  to 
Ch.  XIII,  §  13. 


SECOND  APPROXIMATION  405 

"constant  terms,"  the  left-hand  member  may  be  represented 
by  a  constant  K,  and  the  equation  becomes 

This  is  evidently  the  equation  of  the  straight  line  AB  drawn 
so  that  OA  is  equal  to  /^and  OB  is  equal  to  K  (1  +  i')} 

We  see,  therefore,  that  all  points  on  the  line  AB  drawn  in 
the  manner  described  represent  optional  income-streams  of  equal 
present  values.  The  line  A^B',  parallel  to  AB,  drawn  somewhat 
more  remote  from  the  origin  0,  will  in  like  manner  represent 
the  assemblage  (or  "  locus  ")  of  all  points  which  have  a  present 
value  equal  to  OA'  larger  than  OA} 

§4 

We  see  at  once  that  to  select  the  point,  among  the  entire 
swarm  of  points,  which  has  the  maximum  present  value,  we 
need  simply  find  that  point  which  will  be  on  a  line  parallel  to 
AB  and  removed  as  far  as  possible  from  the  origin  0.  Evi- 
dently such  a  line  is  ah,  tangent  at  t  to  the  boundary  line  p)'tR. 
It  is  evident,  therefore,  that  t  is  the  point  which  possesses  the 
maximum  present  value  out  of  the  entire  mass.  If  the  rate  of 
interest  rises,  the  slope  of  the  line  ah  will  be  steeper  and  the 
point  of  tangency  t  will  shift  toward  the  right.  In  other 
words,  the  option  now  chosen  will  be  one  which  has  a  larger 
y'  but  a  smaller  ?/";  that  is,  a  larger  income  for  the  present 
year  and  a  smaller  one  for  next  year.  On  the  other  hand,  if 
the  rate  of  interest  falls,  the  slope  of  the  line  ah  will  be  more 
nearly  horizontal  and  the  point  of  tangency  will  rise,  making 
y"  larger  and  y*  smaller. 

Not  only  is  it  true  that  t  is  the  point  at  which  the  present 
value  of  the  income  is  a  maximum,  but  it  is  also  true  that  at 
this  point  the  "  marginal  rate  of  return  on  sacrifice "  will  be 
equal  to  the  rate  of  interest.     We  have  seen  that  the  slope  of 

1  See  preceding  footnote. 

2  That  A'B'  will  be  parallel  to  AB  is  evident  from  the  rule  for  con- 
struction, for  OA'  must  equal  a  constant  K',  and  OB'  must  equal 
K'  (1  -Hi')i  therefore  it  is  evident  that,  comparing  the  similar  construc- 
tion for  AB, 

0B_  qB[ 

OA-^^'  ~0A' 
Consequently  A'B'  is  parallel  to  AB. 


406 


APPENDIX   TO  CHAPTER  VIII 


the  line  ab  represents  the  ratio  of  exchange  between  next 
year's  and  this  year's  income,  namely  1  +  i\  In  like  manner 
the  slope,  at  any  point,  of  the  boundary  line  p'tR  represents 
the  ratio  of  the  return  on  sacrifice,  or  1  +  r'.  This  may  be 
seen  clearly  from  Fig.  28,  where  a  slight  variation  from  t"  to  V 
produces  in  y'  a  small  increase  kt',  but  in  y"  a  small  decrease 
ifcf ".     M'  may  be  designated  by  8?/',  and  M"  by  —  %",  and  we 


O 


Fig.  28. 


may  state  that  hy'  represents  a  slight  increase  in  this  year's 
income,  and  —  8^"  the  consequent  slight  decrease  in  next  year's 


income.     The  ratio  of  these  two,  namely 


,  is  what  was 


called  the  marginal  ratio  of  return  to  sacrifice,  or  1  +  r' ;  that  is, 


%' 


=  l  +  r'. 


Returning  to  Fig.  27,  it  is  evident  that  at  the  point  of 
tangency  t  the  slope  of  the  straight  line  ab  will  be  identical 
with  that  of  the  curve  pHR.     In  other  words, 

Whence  it  follows  that  i'  =  r'. 

We  see,  then,  from  the  diagram:  (1)  that  the  point  t  for  a 


SECOND   APPROXIMATION  407 

particular  individual,  with  a  particular  rate  of  interest,  is  de- 
terminate, and  (2)  that  the  point  t  is  the  one  which  corresponds 
with  the  choice  of  maximum  present  value,  where  r'  =  V. 

§5 

We  shall  now  proceed  to  the  consideration  of  the  case  of 
three  years  instead  of  two.  A  geometrical  representation  may 
still  be  used,  by  employing  three  dimensions  and  three  mu- 
tually perpendicular  axes,  OF',  OF",  OY^".  Any  point  P 
will  indicate  a  possible  income-stream  for  the  three  years  ;  for 
its  coordinates  y',  y",  y'"  may  be  taken  to  indicate  the  income- 
installments  for  the  first,  second,  and  third  years  respectively. 
Representing  the  various  options  by  various  points,  we  have  a 
mass  of  points  occupying  three  dimensions,  like  a  swarm  of 
bees,  and  we  wish  to  select  from  this  series  of  points  that  one 
which  has  the  maximum  present  value.  It  is  evident  that  we 
need  not  consider  as  eligible  every  point  in  the  swarm,  but 
need  only  consider  its  boundary,  or  outside  surface.  For,  if 
any  point  P  be  joined  to  the  origin  0  and  prolonged  beyond  P 
to  the  remotest  point  P'  in  the  mass,  it  is  evident  that  P,  hav- 
ing all  of  its  three  coordinates  larger  than  the  coordinates  of  P, 
will  have  necessarily  a  larger  present  value.  Therefore,  the  only 
point  on  the  line  OP  which  needs  to  be  considered  is  P'  farthest 
from  the  origin  0,  or  on  the  surface  bounding  the  swarm. 
Having  restricted  ourselves,  therefore,  to  the  bounding  surface 
as  including  the  effective  range  of  choice,  we  next  ask,  what 
point  on  this  surface  has  the  maximum  present  value.  To 
answer  this  question  we  observe  that  the  assemblage  or  locus 
of  all  points  or  options  which  have  a  given  present  value  V  is 
found  by  drawing  a  plane  cutting  the  three  axes  OT',  OF', 
and  OY'".  The  expression  for  the  present  value  of  the  income- 
stream  is  evidently 

v"                    v'" 
V=  v'  H — - — f  H h  constant  terms. 

If  we  transpose  "  constant  terms "  to  the  left,  and  remember 
that  Fis  for  the  moment  regarded  as  itself  constant,  we  may 
call  the  entire  left-hand  member  a  constant  K,  and  have  the 
equation 


408  APPENDIX   TO  CHAPTER  VIII 

This  is,  in  analytical  geometry,  the  equation  of  a  plane 
which  cuts  the  Y'  axis  at  a  distance  A"  from  the  origin,  and 
cuts  the  T"  axis  at  a  distance  K{1  +  i')  from  the  origin,  and 
the  Y'"  axis  at  a  distance  7i'(l  +  V)  (1  +  i")  from  the  origin. 

Similar  considerations  will  show,  just  as  in  the  case  of  the 
previous  representation  in  two  dimensions,  that  the  farther 
the  plane  is  from  the  origin  0,  the  larger  the  present  value  of 
the  choices  represented  by  points  in  this  plane.  Our  problem, 
therefore,  consists  merely  in  landing  that  point  on  the  bound- 
ing surface  which  is  also  on  the  plane  farthest  from  0  among 
the  parallel  planes  just  drawn.  This  is  evidently  the  point  of 
tangency,  and  may  be  called  t  as  before.  It  is  also  clear  that  a 
change  in  the  rates  of  interest  V  or  i"  will  change  the  slope  of 
the  tangent  plane,  and  therefore  the  point  of  tangency  t. 

The  algebraic  interpretation  of  this  case  will  be  similar  to 
the  algebraic  expression  already  given  for  two  variables. 

When  we  proceed  to  consider  four  or  more  years  instead  of 
simply  two  or  three  years,  the  geometrical  representation  fails 
us,  since  the  mind  has  difficulty  in  picturing  spaces  of  4,  5, 
...  and  m  dimensions. 

§6 

In  order  to  show  how  the  new  equations  which  have  just 
been  expressed  enter  into  the  determination  of  the  problem  of 
interest,  we  construct  Fig.  29,  applying  to  the  case  only  two 
unknown  quantities  y'  and  y".  The  incomes  for  the  third  and 
succeeding  years  are  regarded  for  the  moment  as  fixed.  The 
diagram  refers  to  a  particular  individual,  and  shows  (1)  the 
curve  WPZ,  giving  the  effective  range  of  choice  among  different 
options  open  to  him,  and  (2)  a  series  of  curves  for  total  util- 
ity or  desirability,  as  explained  in  the  Appendix  to  the  pre- 
ceding chapter.  The  line  AB  is  drawn  at  a  slope  equal  to 
1  +  i  and  tangent  to  the  curve  WZ  at  the  point  P.  This 
line  will  be  tangent  to  one  of  the  family  of  desirability  curves 
at  some  point  Q.  P  represents,  out  of  all  the  options,  the  par- 
ticular income-stream  chosen  by  the  individual.  This  income- 
stream  P  is,  of  course,  as  yet  unmodified  by  borrowing  and 
lending  or  buying  and  selling.  The  point  Q  represents  the 
income-stream  as  finally  thus  modified.  The  coordinates  of 
P  are  ?/'  and  y",  and  the  coordinates  of  Q  are  y'  +  x',  y"  -\-  x", 
where  cc'  and  x"  are  the  (algebraic)  additions  to  the  income  y\ 


SECOND  APPROXIMATION 


409 


y"  by  borrowing  and  lending  or  buying  and  selling.  P  and  Q 
thus  represent  graphically  the  double  choice  explained  in  Chap- 
ter VIII.  We  saw  there  that  the  individual  first  chooses,  among 
the  various  eligible  income-streams  of  different  present  values, 
that  which  is  of  maximum  present  value.  WZ  now  represents 
the  series  of  eligible  income-streams,  and  P  the  income-stream 
of  maximum  present  value.  Also,  we  saw  that  after  the  indi- 
vidual had  chosen  this  income-stream  he  modified  it  by  select- 
ing another  income-stream  of  the  same  present  value  but  of 
maximum  desirability.     Q  now  represents  this  final  choice. 

It  is  worth  our  while  in  passing  to  emphasize  that  the  indi- 
vidual would  not  follow  out  this  program  unless  the  final  step 


10203040  5060 '70 


O 


of  modifying  his  income-stream  by  exchange  were  open  to  him. 
For,  if  he  were  shut  off  from  exchange  {i.e.  compelled  to  accept 
P,  unmodified  to  Q),  the  income-stream  of  maximum  present 
value  (P)  would  not  necessarily  be  that  of  maximum  desira- 
bility. In  this  case  the  maximum  desirability  would  evidently 
be  found  at  S,  the  point  of  tangency  between  WZ  and  a  curve 


410  APPENDIX  TO  CHAPTER  VIII 

(not  drawn)  of  desirability,  and /iS  would  be  chosen  instead  of  P. 
The  choice  of  P  is  made  only  if  there  is  freedom  to  replace  it 
immediately  by  Q  of  higher  desirability  although  of  the  same 
present  value. 

The  only  diiference  between  this  determination  of  the  point 
Q  and  that  shown  in  the  Appendix  to  Chapter  VII,  where  we 
assumed  a  fixed  or  rigid  income-stream,  is  that  there  the  point 
P  was  assumed  as  a  fixed  point,  whereas  here  it  is  considered 
as  a  point  of  taugency  to  a  fixed  curve  WZ.  In  the  previous 
chapter,  if  the  rate  of  interest  changed,  the  line  AB  revolved 
about  the  point  P.  Under  our  new  and  more  general  hypoth- 
esis, if  the  rate  of  interest  changes,  the  line  AB  rolls  upon  the 
curve  WZ.  If  the  range  of  choice  is  reduced  and  the  curve 
WZ  is  thereby  restricted  to  smaller  dimensions,  the  diiference 
between  the  two  cases  is  diminished,  until,  as  a  limiting  case, 
we  may  suppose  the  curve  WZ  to  shrink  into  a  point,  when 
the  range  of  choice  disappears  entirely  and  the  present  diagram 
reverts  to  the  one  used  in  the  previous  Appendix. 

If  now  we  consider  the  case  of  three  unknown  quantities 
y\y'\y"\  it  is  only  necessary  to  introduce  three  dimensions, 
replace  the  curve  WZ  by  a  surface,  the  line  AB  by  a  plane, 
and  the  curves  of  desirability  by  successive  surfaces  in  concen- 
tric layers,  as  shown  in  the  Appendix  to  Chapter  VII.  The 
plane  is  now  drawn  tangent  to  the  surface  representing  the 
effective  range  of  choice,  and  the  point  of  tangency  P  repre- 
sents the  income-stream  chosen  among  all  those  eligible,  while 
the  point  upon  this  plane  Q,  at  which  the  plane  is  tangent  to 
one  of  the  desirability  surfaces,  represents  the  income-stream 
as  finally  modified  by  exchange. 

The  previous  discussion  applies  to  one  individual  only. 
When  we  pass  from  the  individual  to  society,  we  can  no  longer 
consider  the  plane  (or  in  two  dimensions,  the  line)  as  fixed  in 
inclination.  The  problem  of  determining  its  inclination  is 
the  problem  of  determining  the  rate  of  interest.  This  is  equiva- 
lent to  determining  the  inclination  at  which  a  series  of  parallel 
planes  (or  lines),  for  different  individuals,  must  be  passed,  each 
tangent  to  its  own  surface  (or  curve)  WZ,  and  such  that  the 
center  of  gravity  of  all  the  Q's  coincides  with  that  of  all  the  P's. 
This  condition  will  evidently  make  the  algebraic  sum  of  all 
the  x"s  zero,  and  likewise  of  the  x"'s,  etc.  In  other  words, 
it  will  make  the  sums  lent  equal  to  those  borrowed. 


SECOND  APPROXIMATION  411 

This  determination  may  be  mentally  represented  by  consid- 
ering the  set  of  parallel  planes  (or  lines)  to  be  first  placed  in 
any  arbitrary  inclination,  corresponding  to  an  arbitrarily 
assumed  rate  of  interest  for  each  year.  Each  of  these  planes 
(or  lines)  will  have  a  P  and  a  Q\  but  unless  the  centers  of 
gravity  of  the  P's  and  of  the  Q's  happen  to  coincide,  the 
algebraic  sum  of  the  a;'-s,  a;"'s,  etc.,  will  not  be  zero,  that  is, 
the  assumed  rates  of  interest  will  not  clear  the  market.  We 
therefore  now  conceive  the  set  of  planes  (or  lines)  to  r<M  on 
their  respective  boundary  surfaces  (or  curves)  WZ,  and  to  roll 
in  unison,  that  is,  so  that  they  may  be  always  mutually 
parallel.  When  such  a  position  is  found  that  the  center  of 
gravity  of  the  P's  coincides  with  that  of  the  Q's,  the  market 
is  cleared  and  the  inclination  of  the  planes  (or  lines)  then 
found  will  represent  the  rate  of  interest.  The  rolling  process 
here  conceived  simply  visualizes  the  process  given  in  Chapter 
VII,  §  7,  of  finding  tentatively  the  rate  of  interest  which  will 
clear  the  market. 

We  see,  then,  from  our  diagrams,  how  the  different  influences 
cooperate  to  determine  the  rate  of  interest,  as  represented  by 
the  common  slope  of  the  parallel  planes  (or  lines).  These 
planes  (or  lines)  have  the  same  slope  as  the  two  curved  sur- 
faces (or  lines)  to  which  each  is  tangent.  There  is  truth, 
therefore,  both  in  the  subjective  and  objective  theory  of 
interest.  That  the  rate  of  interest  is  equal  to  the  subjective 
rates  of  preference  is  indicated  by  the  tangency  of  the  plane 
(or  line)  to  the  desirability  surfaces  (or  curves) ;  that  it  is  equal 
to  the  rate  of  return  on  sacrifice  is  indicated  by  its  tangency 
to  the  surface  (or  curve)  of  effective  range  of  choice.  These 
two  equalities  are  not  incompatible,  as  has  too  often  been 
assumed.  Interest  is  determined  partly  by  objective  or  tech- 
nical factors  which  supply  the  range  of  opportunity  (the 
boundary  surfaces  or  curves) ;  partly  by  subjective  factors 
which  determine  individually  the  choice  (the  desirability 
curves). 

§7 

We  have  now  seen  how,  on  the  simple  hypothesis  that  the 
income-stream,  or  the  group  of  optional  income-streams,  are 
foreknown,  the  problem  of  the  rate  of  interest  may  be  repre- 
sented and  solved,  both  algebraically  and  geometrically.  We 
found  that  two  of  the  interest-determining  conditions  were  based 


412  APPENDIX  TO   CHAPTER  VIII 

on  the  principle  of  finding  a  maximum.  One  of  these  two  con- 
ditions was  that  the  income-stream  selected  should  have  the  max- 
imum present  value ;  the  other  was  that  this  choice  should  be 
modified  by  exchange  so  as  to  secure  the  maximum  desirability. 
We  shall  now  proceed  to  show  that  these  two  conditions  may  be 
united  into  one,  namely,  that  both  of  these  choices  tend  simply 
to  secure  the  one  end  of  maximum  present  desirability.  It  is 
true  that  maximum  present  value  and  maximum  present  de- 
sirability are  not  interchangeable  concepts,  and  we  have  seen 
that  if  an  individual  is,  for  any  reason,  not  free  to  borrow  or 
lend,  his  choice  of  income-streams  will  be  determined  in  a  dif- 
ferent manner;  the  point  of  maximum  desirability  under  these 
circumstances  will  have  nothing  to  do  with  the  straight  line 
PQ,  but  will  be  at  the  point  at  which  the  curve  WPZ  of  effec- 
tive choice  is  tangent  to  a  utility  curve.  But,  given  the  freedom 
to  interchange  parts  of  the  income-stream  at  the  market  rate 
of  interest,  the  individual  will,  under  these  circumstances,  gain 
the  maximum  desirability  by  first  seeking  that  use  of  his  capital 
which  has  the  maximum  present  value,  and  then  modifying  the 
income  thus  obtained  by  the  loan  or  sale  market.  This  sub- 
serviency of  the  principle  of  maximum  present  value  to  the 
principle  of  maximum  desirability  was  made  evident  in  Chapter 
VIII.     It  becomes  very  clear  geometrically. 

In  Fig.  29  the  individual  is  free  to  select  any  point  on  the 
line  PQ,  and  to  place  this  line  at  any  distance  from  the  origin, 
provided  it  passes  through  one  of  the  swarm  of  points  repre- 
senting his  total  range  of  choice,  and  provided  also  that  its 
slope  always  accords  with  the  market  rate  of  interest.  It  has 
already  been  made  clear  that,  wherever  he  places  the  line,  the 
point  upon  it  of  maximum  desirability  is  Q,  where  it  touches 
a  desirability  curve.  It  only  remains  to  show  that  if  the  line 
were  drawn,  not  through  P,  but  through  a  different  point  in 
the  swarm,  while  keeping  the  same  slope,  Q  would  be  a  point 
of  lower  desirability.  This  is  evident,  for  if  PQ  is  not  drawn 
through  P,  its  only  other  possible  position  must  be  parallel  to 
that  position,  but  not  so  far  from  the  origin  0.  But  in  that 
case,  Q  would  evidently  be  on  a  curve  of  lower  desirability, 
since  the  family  of  such  curves  ascends  as  we  recede  from  0. 

§8 

We  may  now  summarize  both  the  geometrical  and  algebraic 
determinations  of  the  rate  of  interest :  — 


SECOND  APPROXIMATION  413 

1.  We  have  the  condition  that,  for  each  individual,  the 
effective  range  of  choice  among  income-streams  is  limited  to 
a  specific  set  of  options,  owing  to  the  technical  limitations  of 
his  capital,  etc. 

Geometrically,  this  condition  is  represented  by  the  surface 
(or  curve)  WZ. 

Algebraically,  this  condition  is  represented  by  n  equations 
of  the  type 

<!>  (y',y",  etc.)  =  0, 

each  relating  to  an  individual. 

2.  We  have  the  condition  that  the  rate  of  preference  for 
each  individual  for  each  yeai",  as  estimated  in  the  present, 
depends  upon  the  future  income-stream  as  indicated  by  its 
annual  installments. 

Geometrically,  this  condition  is  represented  by  the  family 
of  desirability  surfaces  (or  curves).  The  slopes  at  each  point 
correspond  to  the  rates  of  preference,  and  the  coordinates  of 
the  point  correspond  to  the  installments  of  the  income-stream. 
The  fact  that  the  slopes  depend  upon  the  position  of  that  point 
represents  the  fact  that  the  rate  of  preference  depends  on  the 
income-stream. 

Algebraically,  this  condition  is  represented  by  n(in  —  1) 
equations  of  the  type 

f=F(y'-\-x',y"  +  x",etc.), 

each  relating  to  a  single  individual  and  a  pair  of  consecutive 
years. 

3.  We  have  the  condition  that  the  market  rate  of  prefer- 
ence of  each  individual  is  equal  to  the  rate  of  interest  and 
to  each  other ;  or,  equivalently,  that  his  total  desirability  is  a 
maximum. 

Geometrically,  this  condition  is  represented  by  the  fact  that 
at  Q  the  inclination  of  the  plane  (or  line)  is  the  same  as  that 
of  the  desirability  surface  (or  curve)  at  that  point, — in  short, 
that  they  are  there  tangent  and  further  that  the  directions  of 
the  desirability  curves  at  all  the  Q's  are  parallel,  —  in  short, 
that  the  planes  (or  lines)  drawn  tangent  to  them  are  parallel 
to  each  other. 

Algebraically,  these  conditions  are  represented  by  m  —  1 
continuous  equations  of  the  type 

fi  =f-i  =•'•  =/„  =  i, 


414  APPENDIX   TO   CHAPTER  VIII 

each  relating  to  two  successive  years,  making  w(m  —  1)  equa- 
tions in  all. 

4.  We  have  the  condition  that  out  of  the  effective  range 
of  choice,  that  particular  one  of  the  income-streams  is  selected 
which  possesses  the  maximum  present  value,  or,  equivalently, 
that  one  is  selected  such  that,  when  it  is  compared  with  its 
nearest  neighbor,  the  marginal  rate  of  return  on  sacrifice  is 
equal  to  the   rate  of  interest. 

Geometrically,  this  condition  is  represented  by  the  fact  that 
the  plane  (or  straight  line)  AB  is  tangent  to  WZ  for  each 
individual. 

Algebraically,  this  condition  is  represented  by  2w(m  — 1) 
equations,  consisting  of  n(m  —  1)  pairs,  of  which  the  following 
is  the  type 

l  +  i  =  l  +  r  =  if;(y',y",etc.), 

there  being  one  such  double  equation  for  each  individual  for 
each  pair  of  successive  years. 

5.  We  have  the  condition  that  the  sum  added  (by  borrowing 
and  lending,  or  buying  and  selling)  in  any  year  to  the  income 
of  one  individual  is  equal  to  that  taken  from  others,  or,  equiv- 
alently, that  the  algebraic  sum  of  such  modifications  is  zero. 

Geometrically,  this  condition  is  represented  by  the  fact  that, 
for  each  individual,  the  center  of  gravity  of  the  Q's  coincides 
with  that  of  the  P's. 

Algebraically,  this  condition  is  represented  by  m  equations 
of  the  type 

Xi  +  Xo  +  Xs-] h  x„  =  0, 

one  for  each  year. 

6.  We  have  the  condition  that  for  each  individual  the  posi- 
tive and  negative  modifications  of  his  income-stream  in  dif- 
ferent years  mutually  offset  each  other  in  present  value,  or, 
in  more  common  language,  what  is  borrowed  is  repayable  with 
interest. 

Geometrically,  this  condition  is  represented  by  the  fact  that 
for  each  individual,  P  and  Q  lie  in  the  same  plane  (or  straight 
line)  AB. 

Algebraically,  this  condition  is  represented  by  ?i  equations  of 
the  type 

x'  +  — \ h  etc.  =  0, 

^1-Fi'      (l-fi')(l  +  t") 
one  for  each  individual. 


SECOND  APPROXIMATION  415 

Counting  up  the  total  number  of  equations  thus  indicated, 
we  find :  — 

For  the  1st  condition,  n  equations, 

2d  condition,  w(m  —  1)  equations, 
3d  condition,  n(m  —  1)  equations, 

4th  condition,  2  n{m  —  1)  equations, 

5th  condition,  m  equations, 

6th  condition,  n  equations, 

making  a  total  of  Amn  +  m  —  2  ?i  equations, 
of  which,  for  reasons  given  in  the  Appendix  to  Chapter  VII, 
only  Amn -\-m  —  2n  —  l  are  independent  equations. 
The  number  of  unknowns  is  as  follows :  — 

number  of  2/'s  is  mn, 
number  of  x's  is  mn, 
number  of  r's  is  n(m—  1), 
number  of /'s  is  n(m—  1), 
number  of  t's  is  m  —  1, 

the  total  of  which  is  also  4mn  +  m— 2n  —  1.     Hence  the  prob- 
lem of  interest  is  determinate. 

So  much  space  has  been  devoted  to  stating  these  six  condi- 
tions in  mathematical  form,  because,  to  those  conversant  with 
the  mathematical  tongue,  the  algebraic  statement  will  show 
more  definitely  and  clearly  than  is  otherwise  possible  the 
determinateness  of  the  problem,  owing  to  the  equality  between 
the  number  of  equations  and  the  number  of  unknowns;  while 
the  geometrical  method  enables  them  to  form  a  mental  picture, 
clearer  than  would  otherwise  be  possible,  of  the  various  factors 
at  work,  and  especially  of  the  manner  in  which  the  objective 
or  "technical"  conditions,  as  represented  by  WZ,  cooperate 
with  the  subjective  conditions  which  influence  the  rate  of 
interest.  It  was,  in  fact,  only  through  the  geometrical  repre- 
sentation that  the  writer  was  first  enabled  to  grasp  the  signifi- 
cance of  the  "effective  range  of  choice"  in  its  general  bearings. 
If  the  role  of  the  curve  WZ  is  grasped,  the  most  difficult  part 
of  the  theory  of  interest  is  mastered. 


APPENDIX  TO   CHAPTER  XI 

Third  Approximation 
§  1  (TO  Ch.  11,  §  8) 

To  attempt  to  formulate  in  mathematical  language,  in  any 
useful  manner,  the  complete  laws  determining  the  rate  of  in- 
terest under  the  sway  of  chance,  would  be  like  attempting  to 
express  the  complete  laws  which  determine  the  path  of  a  pro- 
jectile when  affected  by  random  gusts  of  wind.  Such  formulae 
would  need  to  be  either  too  general  or  too  empirical  to  be  of 
much  value.  In  science,  the  most  useful  formulae  are  those 
which  apply  to  the  simplest  cases.  For  instance,  in  the  study  of 
projectiles,  the  formula  of  most  importance  is  that  which  ap- 
plies to  the  path  of  a  projectile  in  ideal  vacuum.  Next  come  the 
formulae  which  apply  to  a  projectile  in  still  air.  It  is  seldom 
that  the  mathematician  attempts  to  go  beyond  this,  and  take 
into  account  the  effect  of  wind  currents;  and  if  he  does  so,  he 
still  falls  short  of  actual  conditions,  by  assuming  the  wind  to 
be  constant  in  direction  and  velocity.  The  truth  is  that 
science  always  stops  short  of  the  final  approximation  necessary 
to  reach  reality.  This  is  due  to  the  nature  of  science  itself, 
which  is  a  study  of  what  ivould  happen  under  assumed  condi- 
tions, and  only  an  approximate  application  of  what  does  hap- 
pen under  actual  conditions.^  The  consequence  is  that,  in 
order  to  reach  the  final  goal  of  real  conditions,  we  usually  cut 
the  Gordian  knots  which  remain;  and  for  such  summary  solu- 
tion, especially  when  the  solution  is  general  instead  of  numer- 
ical, ordinary  language  is  usually  better  than  mathematical 
formulae.  Accordingly,  in  treatises  on  projectiles  we  do  not 
find  any  attempt  to  state  their  trajectories  in  general  formulae 
which  include  the  effects  of  gusts  of  wind.  Still  less  is  there 
any  attempt  to  construct  a  formula  for  the  path  of  a  boomer- 
ang or  of  a  feather  thrown  out  of  a  window. 

To  apply  the  analogy  to  the  problem  in  hand,  we  have 
already  stated  the  laws  determining  interest  under  the  simpler 

1  See  the  writer's  "Economics  as  a  Science,"  in  Science,  Aug.  31,  1906. 

416 


THIRD  APPROXIMATION  417 

conditions,  —  first,  when  it  was  assumed  that  the  income- 
streams  of  individuals  were  both  certain  and  fixed,  and, 
secondly,  when  it  was  assumed  that  the  income-streams  were 
certain,  but  flexible.  When  we  introduce  the  element  of  un- 
certainty, our  formulae  cease  to  have  the  characteristics  of 
simple  clarifying  shorthand  which  justify  their  use,  and  take 
on  the  characteristics  of  what  Marshall  calls  the  "lengthy- 
translations  of  political  economy  into  mathematics."  While, 
therefore,  it  is  not  difficult  to  make  these  translations,  they 
add  little  or  nothing  to  our  understanding  of  the  problem. 
Inasmuch  as  it  is  our  aim  to  employ  mathematics  only  when 
they  add  something  which  cannot  be  conveyed  without  their 
use,  we  refrain  from  wearying  the  reader  with  cumbersome 
equations. 


2e 


APPENDIX  TO  CHAPTER  XIV 

Statistical  Data 

§1 

The  writer  has  found  so  much  difficulty  in  securing  a  long 
series  of  yearly  averages  for  rates  of  interest  that  the  results 
are  here  presented  in  the  hope  that  they  may  be  of  use  to 
others. 

YEARLY  AVERAGE  RATES  OF    INTEREST » 


London 

Berlin 

Paris 

New  York 

Calcutta 

Tokyo 

Shanghai 

c 

0) 

3 

a 

1 

CO 

o 
* 

Prime 
2  Name 
60  Days 

4«1 

C 
el 

cq 

3 

e 

ct 

1824 
1825 
1826 
1827 
1828 
1829 
1830 
1831 
1832 
1833 
1834 
1835 
1836 
1837 
1838 
1839 
1840 
1841 
1842 
1843 

.5 
.9 
.5 
.3 
3.0 
3.4 
2.8 
3.7 
3.1 
2.7 
3.4 
3.7 
4.2 
4.5 
3.0 
5.1 
5.0 
4.9 
3.3 
2.2 

4.0 
4.0 
5.0 
4.5 
4.0 
4.0 
4.0 
4.0 
4.0 
4.0 
4.0 
4.0 
4.4 
5.0 
4.1 
5.1 
5.1 
5.0 
4.3 
4.0 

• 

1  The  London,  Berlin  and  Paris  market  rates  are  on  first  class 
merchants'  bills.  The  figures  for  1824-58  are  from  the  evidence  of  D.  B. 
Chapman  before  the  Committee  on  the  Bank  Act,  1857,  Sess.  2,  X,  pt.  I, 
p.  463  (also  reprinted  in  HunVs  Merchants'  Magazine,  Vol.  41  (1859), 
p.  95).  The  remaining  figures  are  compiled  from  the  Economist.  For 
those  for  1884-94,  the  writer  is  indebted  to  Professor  F.  M.  Taylor  of 
Michigan  University,  who  had  collected  them  from  the  Economist  for  a 
different  purpose.  The  Bank  of  England  rates  for  1824-43  are  reduced 
from  "  Burdett's  Official  Intelligencer"  (1894),  p.  1771.  The  remaining 
ones  for  England,  Germany,  and  France  are  reduced  from  those  given  in 
the  Report  of  the  Royal  Commi-ssion  on  Depression  of  Trade,  1886,  p.  373, 
and  the  ^conomtsi.  They  represent  the  bank  "minimum."  The  rates 
1896-1903  are  from  A.  Sauerbeck's  tables,  Journal  Boyal  Statistical 
Society,  Vol.  LXVII,  Part  I,  p.  89.     The  New  York  rates  are  taken,  the 

418 


STATISTICAL   DATA 


419 


YEARLY  AVERAGE  RATES  OF  INTEREST  —  Con^mwed 


London 

Berlin 

Paris 

New  Toek 

Calcutta 

Tokyo 

Shanghai 

-4J 
it 

1 

c 

2 

a 
a 

Jt 

Q 

4.5 
4.8 
5.9 
5.1 
6.9 
7.7 

Prime 
2  Name 
60  Days 

c 

pa 

1 

it 

0 
it 
a 

J4 

a 

1844 
1845 
1846 
1847 
1848 
1849 
1850 
1851 
1852 
1853 
1854 

2.1 
3.0 
3.8 
5.9 
3.2 
2.3 
2.2 
3.1 
1.9 
3.7 
4.9 

2.52 

2.7 
3.3 
5.2 
3.7 
2.9 
2.5 
3.0 
2.2 
2.7 
2.1 

■    ■ 

4.3 

4.4 
4.7 
4.8 
4.7 
4.0 
4.0 
4.0 
4.0 
4.2 
4.3 

4.0 
4.0 
4.0 
4.9 
4.0 
4.0 
4.0 
4.0 
3.2 
3.2 
4.3 

7.S 
7.2 
8.3 
7.3 
10.1 
12.5 

3.9 

first  two  columns,  from  a  table  by  E.  B.  Elliott  (afterward  government 
actuary)  in  the  (New  York)  Banker's  Magazine,  1874.  The  quotations 
given  as  "60  days"  apparently  included  single  name  paper.  The  third 
column  to  1890  is  compiled  from  a  diagram  of  highest  and  lowest  monthly 
rates  prepared  at  Yale  College  by  Mr.  G.  P.  Robbins  of  the  class  of  1891, 
and  has  been  completed  from  the  Financial  Review,  by  averaging  the 
highest  and  lowest  weekly  rates.  It  has  been  found  impossible  to  extend 
the  New  York  table  back  beyond  1849,  as  the  rates  are  not  systemati- 
cally reported.  The  Calcutta  rates  are  the  minimum  of  the  Bank  of 
Bengal  and  have  been  kindly  furnished  by  Messrs.  Place,  Siddons,  and 
Gough,  brokers,  of  Calcutta.  The  market  rates  of  Tokyo  are  averages 
of  the  highest  and  lowest  rates  of  each  year,  furnished  by  Mr.  Ichi 
Hara  of  the  Bank  of  Japan,  Tokyo.  The  bank  rates  are  for  the  Tokyo 
and  Yokohama  Cooperative  Bank  and  were  translated  by  Mr.  Sakata, 
student  at  Yale,  from  a  history  of  Japan  by  Zen.shiro  Tsuboya.  The 
continuation  of  the  table  after  1895  has  been  supplied  by  Mr.  Hitomi, 
one  of  my  students,  and  is  based  upon  :  Financial  Report  of  the  De- 
partment of  the  Treasury,  Reports  Tokyo  Economic  Magazine  Pub- 
lishing Co.,  Reports  Tokyo  Bankers'  Association,  and  Reports  of 
Department  of  Agriculture  and  Commerce.  (The  last  three  sources 
are  in  Japanese  only.)  The  tables  for  Shanghai  have  been  procured 
through  the  kindness  of  Prof.  F.  W.  Williams  of  the  department  of 
Oriental  History  of  Yale  College,  who  obtained  them  from  Mr.  J.  F. 
Seaman  of  Shanghai.  The  first  column  contains  the  rates  ruling  in  the 
native  market,  and  the  second,  those  of  the  Hong  Kong  and  Shanghai 
bank  (under  English  control)  on  overdrawn  current  accounts,  a  species 
of  demand  loans  and  the  ordinary  form  of  lending  in  Shanghai.  Mr. 
Seaman  was  told  that  the  market  rates  cannot  be  extended  back  beyond 
1885,  as  the  books  of  the  Chinese  banks  for  previous  years  are  burnt. 

2  This  rate  is  only  from  September,  when  the  operation  of  the  Bank 
Act  began.     Previous  to  this  the  custom  of  the  bank  was  to  have  a  uni- 
orm  rate  for  all  loans. 


420 


THE  RATE  OF  INTEREST 


YEARLY  AVERAGE  RATES  OF  INTBRBST  —  Concluded 


London 

Berlin 

Paris 

New  York   U 

ALCUT 

TA  Tokyo 

Shanghai 

-4.9 

c 

pq 

4.> 

a 

3 

J4 

a 
a 

P9 

"3 

Prime 
2  Name 
60  Days 

1                  1 

B3 

a 

a 

M 

i> 
15 

a 

1855 

4.7 

2.9 

4.1 

4.5 

6.6 

9.3  ... 

9.7 

1856 

5.9 

6.1 

4.9 

5.5 

7.0 

9.9  ... 

6.5 

,   ^ 

,   , 

,   , 

1857 

7.1 

6.7 

5.8 

6.1 

6.9 

10.4  .  .  . 

7.0 

. 

.   , 

,   , 

1858 

3.1 

3.2 

4.5 

3.7 

3.8 

6.7  ... 

6.1 

,   , 

»   , 

,   , 

1859 

2.5 

3.7 

4.2 

3.5 

5.0 

7.2  ... 

4.9 

w 

,   , 

•   • 

1860 

4.1 

4.2 

4.0 

3.6 

6.1 

8.4   7.7 

4.2 

1-1  Hft 

,   , 

,   , 

1861 

5.5 

5.3 

3.6 

4.0 

5.5 

5.4 

9.0   6.6 

4.2 

to  o 

2  1-' 

,   , 

•   • 

1862 

2.4 

2.5 

3.0 

4.0 

3.8 

5.6 

6.{ 

5   5.4 

5.1 

,   , 

,   , 

1863 

4.3 

4.4 

3.5 

4.1 

4.6 

5.0 

6.' 

I      5.8 

5.5 

9^ 

,   , 

.  . 

1864 

7.4 

7.4 

5.1 

5.3 

6.5 

7.2 

9.: 

$   8.0 

8.7 

,   , 

^   , 

1865 

4.6 

4.8 

4.6 

5.0 

3.7 

6.1 

lO.i 

I      8.2 

6.9 

^K 

,   , 

•   • 

1866 

6.7 

6.9 

6.2 

6.2 

3.7 

5.9 

7.J 

I      6.3 

9.1 

•  o 

,   , 

13. 

1867 

2.3 

2.6 

2.9 

4.0 

2.7 

5.9 

8.'; 

7      7.2 

5.1 

o 

,   , 

11. 

1868 

1.8 

2.1 

2.5 

4.0 

2.5 

5.8 

8.{ 

i      7.3 

5.8 

15. 

18. 

12. 

1869 

3.0 

3.2 

3.2 

4.1 

2.5 

6.0 

lO.J 

i      9.1 

6.0 

18. 

18. 

12. 

1870 

3.1 

3.1 

4.5 

4.8 

4.0 

5.1 

8.] 

L   7.2 

5.7 

18. 

18. 

11. 

1871 

2.7 

2.9 

3.8 

4.2 

5.7 

4.5 

6.( 

)   6.1 

4.7 

14. 

18. 

12. 

1872 

3.8 

4.1 

4.0 

4.3 

4.2 

5.1 

5.6 

9.{ 

)   8.0 

5.0 

14. 

18. 

10. 

1873 

4.5 

4.8 

4.5 

5.0 

5.0 

5.2 

6.3 

9.5 

i     10.3 

3.9 

14. 

14. 

10. 

1874 

3.5 

3.7 

3.3 

4.4 

4.0 

4.3 

3.9 

a.'^ 

t   6.0 

6.2 

12. 

14. 

10. 

1875 

3.0 

3.2 

3.7 

4.7 

3.2 

4.0 

.   5.5 

5.7 

12. 

14. 

9. 

1876 

2.2 

2.6 

3.1 

4.1 

2.3 

3.4 

.   5.2 

6.8 

12. 

15. 

9.5 

1877 

2.3 

2.9 

3.3 

4.4 

1.8 

2.3 

.   5.2 

8.4 

10. 

13. 

9.5 

1878 

3.5 

3.8 

3.4 

4.3 

2.0 

2.2 

.   4.8 

5.3 

11. 

15. 

9. 

1879 

1.8 

2.5 

2.7 

3.7 

2.2 

2.6 

.   5.0 

6.3 

11. 

16. 

9. 

1880 

2.2 

2.8 

3.1 

4.2 

2.5 

2.8 

.   5.2 

4.6 

13. 

17. 

8.5 

1881 

2.9 

3.5 

3.4 

4.4 

3.7 

3.9 

.   5.2 

5.3 

14. 

17. 

8. 

1882 

3.4 

4.1 

3.9 

4.5 

3.4 

3.8 

.   5.7 

6.6 

10. 

17. 

8. 

1883 

3.0 

3.6 

3.1 

4.1 

2.6 

3.1 

.   5.5 

6.8 

7.9 

11. 

8. 

1884 

2.6 

3.0 

2.9 

4.0 

2.4 

3.0 

.   5.2 

6.4 

12. 

16. 

8. 

1885 

2.0 

2.9 

2.9 

4.1 

2.5 

3.0 

. 

.   4.1 

5.4 

13. 

11. 

4.6 

7.5 

1886 

2.1 

3.0 

2.1 

3.3 

2.2 

3.0 

.   4.7 

6.0 

8.8 

9.2 

6.1 

7. 

1887 

2.4 

3.3 

2.3 

3.4 

2.4 

3.0 

.   5.7 

5.6 

9.0 

8.8 

6.5 

7. 

1888 

2.4 

3.3 

2.1 

3.3 

2.8 

3.3 

.   4.9 

5.5 

10. 

9.7 

6.0 

7. 

1889 

2.7 

3.6 

2.7 

3.7 

2.6 

3.1 

.   4.8 

7.0 

10. 

10. 

6.2 

7. 

1890 

3.7 

4.5 

3.7 

4.5 

2.6 

3.0 

6.0 

5.8 

11. 

11. 

7.2 

7. 

1891 

2.5 

3.3 

3.0 

3.9 

2.6 

3.0 

5.7 

3.1 

9.4 

9.4 

3.5 

7. 

1892 

1.5 

2.5 

1.8 

3.2 

1.8 

2.7 

4.3 

3.5 

8.3 

8.4 

5.0 

7. 

1893 

2.1 

3.1 

3.2 

4.1 

2.2 

2.5 

7.1 

4.9 

7.8 

7.8 

6.9 

7. 

1894 

1.0 

2.1 

1.7 

3.1 

1.8 

2.5 

3.4 

5.4 

9.3 

9.4 

3.8 

7. 

1895 

.8 

2.0 

2.0 

3.1 

1.6 

2.1 

3.8 

4.3 

9.6 

9.6 

2.8 

6.5 

1896 

1.4 

2.5 

3.0 

3.7 

1.8 

2.0 

5.8 

. 

11.0 

9.3 

.  . 

1897 

1.8 

2.6 

3.1 

3.8 

1.8 

2.0 

3.4 

, 

11.4 

9.9 

,   , 

1898 

2.6 

3.3 

3.6 

4.3 

2,1 

2.2 

3.8 

. 

12.3 

11.4 

. 

1899 

3.3 

3.8 

4.5 

5.0 

3.0 

3.1 

4.2 

, 

10.4 

8.8 

,   ^ 

1900 

3.7 

4.0 

4.4 

5.3 

3.2 

3.3 

4.4 

, 

12.1 

10.8 

. 

1901 

3.2 

3.8 

3.1 

4.1 

2.5 

3.0 

4.4 

, 

13.1 

11.9 

.  . 

1902 

3.0 

3.3 

2.2 

3.3 

2.4 

3.0 

4.9 

, 

12.1 

10.4 

.  . 

1903 

3.2 

3.8 

3.0 

3.8 

2.8 

3.0 

5.5 

, 

10.7 

,   , 

,   , 

1904 

2.7 

3.3 

3.1 

4.2 

2.2 

3.0 

4.2 

, 

10.8 

,   , 

.  . 

1905 

2.6 

3.0 

2.9 

3.8 

2.1 

3.0 

4.3 

, 

,   , 

,   , 

1906 

4.0 

4.2 

4.0 

5.1 

2.7 

3.0 

5.7 

• 

•  • 

•  • 

•  • 

STATISTICAL  DATA  421 

All  the  rates  in  the  foregoing  table  are  entered  as  rates  of 
"  interest,"  though  the  rates  for  the  Banks  of  England,  Ger- 
many, and  France  are  rates  of  discount.  Although  the  two 
are  not  quite  equivalent,  for  the  purposes  of  the  foregoing 
work  the  distinction  between  them  is  unnecessary,  because, 
in  a  continuous  series,  the  error,  if  any,  affects  all  items 
nearly  alike  and  thus  cancels  itself   out  in  the  comparisons. 

Had  it  been  necessary,  some  of  the  tables  could  have  been 
extended  backward.  Thus  the  Bank  of  England  rate  could 
be  given  as  far  back  as  1696,  but  it  was  too  inflexible  to  be 
of  use.  The  Berlin  and  Paris  bank  notes  could  also  be  ex- 
tended and  the  Paris  market  rate  could  be  given  back  to  1861 
(except  for  1870  and  1871)  from  data  in  the  Economist. 

Many  of  the  sources  from  which  the  table  has  been  drawn 
also  contain  other  information  such  as  the  rates  for  other 
money  centers  than  those  named,  the  weekly  or  monthly 
rates,  the  variation  with  the  seasons,  etc. 

§2 

Of  sources  not  mentioned  in  the  above  note,  the  chief  which 
the  writer  has  encountered  are :  — 

Eleventh  Census  of  the  United  States,  Bulletin  71  (on  real  estate  mort- 
gages, 1880-89). 

This  is  probably  the  most  elaborate  series  of  interest  averages  ever  con- 
structed. 

Twelfth  Census  of  the  United  States,  Special  Eeports,  wealth,  debt,  and 
taxation,  pp.  143,  147,  394.    Rates  of  interest  on  public  debts. 

"Commercial  Valuation  of  Railway  Operating  Property  in  the  United 
States,  1904,"  United  States  Census  Bulletin  21  (1905). 

Gives  rates  of  return  on  railway  securities  to  investor  for  1904. 

Reports  of  the  Secretary  of  the  Treasury. 
Reports  of  the  Comptroller  of  Currency. 

The  last  two  references  contain  statistics  of  rates  of  interest  realized  on 
some  United  States  Government  bonds. 

R.  A.  Bayley,  "National  Loans  of  the  United  States"  (Government 
Printing  Office,  Washington,  1882). 

Gives  rates  of  interest  and  price  of  issue  of  all  United  States  loans  from 
July  4, 1776,  to  June  30, 1880. 

Report  of  the  New  England  Mutual  Life  Insurance  Company,  Boston, 
1890. 

Gives  rates  realized  by  twenty  representative  insurance  companies  for 
186i>-88,  and  for  Massachusetts  savings  banks  for  1877-89,  and  bank  divi- 


422  THE  RATE   OF  INTEREST 

dends  in  Boston,  New  York  and  Philadelphia.  The  rates  realized  by  the 
insurance  companies  for  the  twenty  years,  18(;i>-88,  inclusive,  were  6.0,  5.9, 
6.1,  6.2,  6.5,  6.2,  6.5,  6.1,  5.6,  5.1,  5.0,  4.8,  4.8,  5.1,  5.1,  4.7,  4.7,  4.9,  4.7,  4.6, 
respectively.  These  represent  (if  the  writer  mistakes  not)  the  average  rates 
earned  on  the  par  value  of  investments  of  all  ages,  some  old,  some  new, 
some  terminable  soon  and  others  having  many  years  to  run.  For  this 
reason  they  are  of  little  or  no  use  for  the  purposes  of  Chapter  XIV. 

Lester  W.  Zartman,  The  Investments  of  Life  Insurance  Companies,  New 
York  (Henry  Holt  &  Co.),  1906. 

Gives  earning  rate  of  real  estate,  mortgage  loans  and  bonds  and  stocks 
of  the  principal  life  insurance  companies  of  the  United  States  1860-1904, 
and  similar  data  for  companies  of  England,  Canada,  Australia  and  other 
countries. 

W.  B.  Hedge,  "  On  the  Rates  of  Interest  for  the  Use  of  Money  in  Ancient 
and  Modern  Times.  Part  I."  Association  Magazine.,  Vol.  6  (1857), 
pp.  301-333. 

H.  W.  Farnam,  "Some  Effects  of  Falling  Prices,"  Yale  Review,  August, 
1895. 

F.  M.  Taylor,  "Do  we  want  an  Elastic  Currency?"  Political  Science 
Quarterly,  March,  1896,  pp.  133-157. 

Gives  diagram  showing  the  relation  of  surplus  reserves  and  rates  of  dis- 
count ;  also  seasonal  variation  of  rate  of  discount. 

Carl  C.  Plehn,  "Notes  concerning  the  Rates  of  Interest  in  California," 
Publications  American  Statistical  Association,  Vol.  VI  (September 
1899),  p.  350. 

B.  M.  Breckenridge,  "Discount  Rates  in  the  United  States,"  Political 
Science  Quarterly,  Vol.  XIII  (March,  1898),  p.  119. 

R.  H.  Inglis  Palgrave,  Aiialysis  of  the  Transactions  of  the  Bank  of  Eng- 
land (London,  1874). 

Gives  rates,  1844-72,  and  seasonal  variation,  1844-56  and  1857-72.  Shows 
dependence  of  rate  on  ratio  of  reserve  to  liabilities. 

R.  H.  Inglis  Palgrave,  Bank  Bate  and  the  Money  Market  in  England, 
France,  Germany,  Holland  and  Belgium,  1844-1900.  New  York 
(Dutton),  1903. 

Gives  bank  and  market  rates,  with  special  reference  to  variability  in 
England,  France,  Germany,  Holland  and  Belgium. 

W.  Stanley  Jevons,  Investigations  in  Currency  and  Finance  (London, 
1884). 

Contains  diagram  for  prices  of  consols  and  3  per  cent,  stock  from  1731, 
and  minimum  rate  of  interest  in  London  from  1824  ;  also  monthly  varia- 
tion in  rate  of  interest,  p.  10.  The  diagram  for  the  price  of  consols  shows 
that  during  the  middle  and  first  half  of  the  eighteenth  century  the  interest 
realized  was  almost  as  low  as  in  the  present  generation.  It  is  interesting 
to  note  that  this  was  a  period  of  falling  prices. 

Robert  Giffen,  Essays  in  Finance,  second  series  (London,  1886),  p.  37. 
Seasonal  variations  of  interest  in  connection  with  bank  reserves,  etc. 


STATISTICAL  DATA  423 

Arthur  Crump,  English  Manual  of  Banking  (4th  ed.,  London,  1879), 
pp.  141-144. 

Gives  Bank  of  England  rates  for  1694-1876. 
George  Clare,  Money  Market  Primer,  2d  ed.  (London,  1905). 

Diagrams  for  seasonal  variations  of  interest,  bank  reserves,  etc. 
M.  G.  MuUhall,  Dictionary  of  Statistics  (London,  1892),  pp.  76,  607. 

Gives  rates  for  countries  of  Europe  by  five  and  ten  year  periods  since 
1850. 

William  Farr,"On  the  Valuation  of  Railroads,  Telegraphs,"  etc.,  Journal 
of  the  Royal  Staiislical  Society,  September,  1876,  pp.  464-530. 

Rates  of  Discount  and  Exchange,  Banks  of  England,  France,  Prussia, 
Vienna,  1851-1885.  Final  Report  Gold  and  Silver  Commission,  Par- 
liamentary Blue  Book,  1888,  appendix,  p.  207. 

Commercial  and  Financial  Statistics  of  British  India.  (Government 
Printing  Office,  Calcutta.) 

Monthly  Discount,  Bank  of  Bengal,  from  1861,  and  average  quotations  of 
government  securities  held  in  Loudon. 

Tooke,  History  of  Prices,  and 

Tooke  and  Newmarch,  History  of  Prices  from  1793  to  1S56. 

J.  Liegeois,  Essai  sur  Vhistoire  et  la  legislation  de  Viisure  (Paris,  1863). 

Saugrain  (Gaston),  La  haisse  du  taux  de  Vinteret  —  causes  et  consequences 

(Paris,  Larose,  1800) . 
Boucher,  P.  B.,  Histoire  de  Vusure  ches  les  Egyptiens,  les  Orecs,  les 

Bomains,  nos  au  cetres  et  les  Chinois  (Paris,  1806,  1819). 
Alph.  Courtois,  fils,  Histoire  des  Banques  en  France  (Paris,  1881). 
Gives  rate  of  interest  at  the  Bank  of  France,  1800, 

Viscomte  G.  D'Avenel,  Histoire  economique  de  la  propriete,  des  Salaires, 
des  Denrees  et  de  tous  les  Prix  en  general  depuis  Van  1200  jusqu'' en  Van 
1800  (Paris,  1894),  vol.  II,  p.  882. 

This  work  contains  also  tables  of  the  purchasing  power  of  money. 
Dictionaire  des  Finances,  Article  "Interet." 
Gives  rates  at  which  France  has  borrowed. 

Jahrbiicher  fur  Nationalokonomie  und  Statistik,  February,  1896,  pp. 
282-83. 

Gives  bank  and  market  rates  for  London,  Paris,  Berlin,  Amsterdam, 
Brussels,  Vienna  and  St.  Petersburg,  1841-80  by  decades,  and  1881-95  by 
years. 

Handworterbuch  der  Staatsioissenschaften,  Articles  "Banken"  and 
"Zinsfuss." 

Gives  rates  for  Bank  of  Prussia  and  Germany,  1847-89  ;  also  for  Bank 
of  Austria,  1878-89;  Switzerland,  188;i-88. 

Adolf  Soetbeer,  Materiallen  zur  Wdhrungsfrage  (Berlin,  1886),  p.  78. 

Covers  1851-85  for  Banks  of  England,  France  and  Germany  and  market 
rates  of  Hamburg  and  Vienna. 


424  THE  RATE  OF  INTEREST 

Gustav  SchraoUer,  Grundriss  der  Allgemeinen  Volkswirtschaftslehre, 
Leipslc  (Duncker  und  Humblot),  1904,  pp.  206-208. 

Gives  resume  of  course  of  interest  rates  from  ancient  to  modem  times. 
Also  gives  interest  rates,  London,  Paris,  Berlin,  Amsterdam,  Vienna,  New 
York,  and  St.  Petersburg. 

Billeter,  Gesckichte  des  Zinsfusses  im  Griechisch-Bdmischen  Altertum  bis 
auf  Justinian  (Leipsic,  February,  1898). 

"  According  to  the  recent  researches  of  Billeter,  the  normal  rate  of  inter- 
est on  good  security  during  the  period  of  greatest  prosperity  in  Athens  was 
about  12  per  cent. ;  while  in  Rome  at  the  close  of  the  Republic  it  had  fallen 
to  between  4  and  6  per  cent.  Starting  in  again  during  the  early  middle 
ages  at  a  rate  of  20  per  cent,  and  15  per  cent.,  it  gradually  fell,  until  in  the 
great  financial  centers  of  Holland  towards  the  close  of  the  eighteenth  cen- 
tury it  reached  a  rate  of  between  2  per  cent,  and  3  per  cent."  —  From 
Principles  of  Economics,  by  Seligman,  N.Y.  (Longmans),  li)05,  p.  404. 

E.  Laspeyres,  Geschichte  der  volkswirthschaftUchen  Ansichten  der  Nieder- 
Idiider,  Leipsic,  1863.  (Preisschriften  der  f.  Jablonowskischen  Gesell- 
schaft,  Bd.  XI.)     [Contains  Zins  oder  Wucher  ;  pp.  256  ff.] 

Austrian  Government,  Tabellen  zur  Wdhrungsfrage  (Vienna,  1892), 
pp.  204-206.     (Second  edition,  1896,  and  third  edition,  1903,  4.) 

Covers  rates  since  1861  for  banks  of  Italy,  Englaud,  France,  Germany, 
Austria,  Belgium,  and  Holland,  and  market  rates  in  Vienna  since  1869. 

Wilhelni  von  Lucam,  Die  Oesterreichische  Nationalhank  wdhrend  der 
Dauer  des  dritten  Privilegiums  (Vienna,  1876) . 

Gives  rates  for  Bank  of  Austria,  1817-75. 
Theodor  Hertzka,  Wdhrung  und  Handel  (Vienna,  1876). 

Gives  the  number  of  weeks  each  rate  lasted  for  the  Banks  of  England, 
France,  Germany,  and  Austria  during  1844-73. 

G.  Winter,  "Zur  Geschichte  des  Zinsfusses  in  Mittelalter,"  Zeitschrift 

fur  Social  und  Wirtschaftsgeschichte  (Weimar),  1875,  IV,  2;  1896,  IV, 

161. 
W.  J.  Streuber,  Der  Zinfuss  bei  den  B'dmern,  eine  historischantiquarische 

Abhandlung  (Basel,  1857). 
J.  Kahn,   Geschichte  des  Zinfusses  in  Deutschland  seit   1815  und  die 

Ursachen  seiner  Veranderung .     (Stuttgart,  J.  A.  Gotta,  1893.) 
M.  Newmann,  Geschichte  des  Wuche7-s  in  Deutschland  bis  sur  Begrun- 

dung  der  heutigen  Zinsgesetze  (1654).     Halle,  1865. 
Sombart :  Der  Moderne  Kapitalismus,  I,  219. 

Gives  the  following  table  showing  the  rise  in  price  of  a  rent  of  one  mark 
(in  rent  purchase)  in  Frankfurt  a.  M. :  in  1304,  14-15  Marks ;  1314-1315, 
16-17  Marks ;  1323-1327,  18  Marks ;  1333,  19  Marks  ;  1358,  24  Marks. 

Rodbertus,  "  Ein  Versuch,  die  Hohe  des  antiken  Zinsfusses  zu  erklaren." 

Jahrb.  f.  Nat.  Oek.,  Bd.  XLII  (Jena,  1884). 
J.  Conrad,  Politische  Oekonomie,  Jena  (Gustav  Fischer),  1905,  p.  175. 

Gives  rates  of  discount  1871-1904  in  London,  Paris,  Berlin,  Vienna,  and 
St.  Petersburg, 


STATISTICAL  DATA 


425 


A.  N,  Kiaer,  Om  seddelbanker  (Kristiania,  1877). 

Contains  diagram  of  bank  rates  at  Kristiania,  Stockholm,  and  Kjoben- 
harn,  1853-76. 

J.  P.  Norton,  Statistical  Studies  in  the  New  York  Money  Market,  New 
Haven  (Tuttle,  Morehouse,  and  Taylor),  1903. 

Financial  and  Economical  Annual  of  Japan,  Tokyo,  Government  Print- 
ing Office. 

§3 

The  following  tables  of  index  numbers  are  appended  in 
order  that  the  reader  may  verify  the  periods  of  rising  and 
falling  prices  which  have  been  discussed  in  Chapter  XIV  and 
for  the  reason  that  many  of  the  tables,  notably  those  for  In- 
dia, Japan  and  China,  have  not  been  easily  accessible  to  most 
readers. 

INDEX   NUMBERS  OF  PRICES  IN  SEVEN  COUNTRIES  ^ 


England 

Germany 

Fkanck 

United 

8TATK8 

India 

Japan 

China 

1824  .  .  . 

105 

124 

108 

108 

97 

95 

97 

98 

93 

90 

93 

96 

103 

101 

101 

110 

104 

102 

90 

85 

83 

89 

89 

94 

82 

77 

77 

79 

781 

95 

102 

101 

1825  .  . 

1826  .  . 

1827  .  . 

1828  .  . 

1829  .  . 

1830  .  . 

1831  .  . 

1832  .  . 

1833  .  . 

1834  .  . 

1835  .  . 

1836  .  . 

1837  .  . 

1838  .  . 

1839  .  . 

1840  .  . 

98 
98 
90 
84 
85 
88 
95 
95 
88 
83 
89 
99 
98 
105 
105 
109 

1841  .  . 

1842  .  . 

1843  .  . 

1844  .  . 

1845  .  . 

1846  .  . 

1847  .  . 

1848  .  . 

1849  .  . 

1850  .  . 

1851  .  , 

100 
102 
114 
121 
124 

1852  .  . 

1853  .  . 

1854  .  . 

1855  .  . 

426 


THE   RATE   OF  INTEREST 


INDEX  NUMBERS  OF  PRICES  IN  SEVEN  COUNTRIES  —  ConcZiided 


England 

Gehmany 

France 

United 

States 

India 

Japan 

China 

1856  .  . 

101 

123 

112 

1857  .  . 

105 

130 

114 

.... 

1858  .  . 

91 

114 

113 

.... 

1859  .  . 

94 

116 

103 

.... 

1860  .  . 

99 

121 

100 

.... 

1861  .  . 

98 

118 

100 

94 

•   •   •   • 

1862  .  . 

101 

123 

118 

104 

.... 

1863  .  . 

103 

125 

127 

132 

.... 

1864  .  . 

105 

129 

129 

172 

■   •   •   • 

1865  .  . 

101 

123 

112 

232 

.... 

1866  .  . 

102 

126 

115 

188 

.... 

1867  .  . 

100 

124 

100 

166 

.... 

1868  .  . 

99 

122 

95 

174 

•   •   *   > 

1869  .  . 

98 

123 

97 

152 

•   •   •   • 

1870  .  . 

96 

123 

94 

144 

.... 

1871  .  . 

100 

127 

94 

136 

•   •   •   • 

1872  .  . 

109 

136 

105 

132 

■   *   •   • 

1873  .  . 

111 

138 

103 

129 

100 

104 

1874  .  . 

102 

136 

94 

130 

98 

104 

100 

1875  .  . 

96 

130 

87 

129 

95 

105 

103 

1876  .  . 

95 

128 

85 

123 

99 

102 

111 

1877  .  . 

94 

128 

82 

114 

121 

105 

101 

1878  .  . 

87 

121 

78 

105 

125 

114 

106 

1879  .  . 

83 

117 

76 

95 

119 

145 

111 

1880  .  . 

88 

122 

79 

105 

112 

160 

105 

1881  .  . 

85 

121 

76 

108 

99 

175 

110 

1882  .  . 

84 

122 

73 

109 

98 

159 

108 

1883  .  . 

82 

122 

73 

107 

96 

130 

103 

1884  .  . 

76 

114 

72 

103 

97 

116 

104 

1885  .  . 

72 

109 

70 

93 

95 

116 

105 

1886  .  . 

69 

104 

69 

93 

99 

107 

107 

1887  .  . 

68 

102 

71 

94 

101 

109 

105 

1888  .  . 

70 

102 

74 

96 

104 

112 

100 

1889  .  . 

72 

106 

80 

98 

107 

116 

105 

1890  .  . 

72 

108 

83 

94 

103 

124 

104 

1891  .  . 

72 

1091 

79 

94 

104 

123 

104 

1892  .  . 

68 

106 

89 

115 

124 

108 

1893  .  . 

68 

102 

89 

119 

129 

109 

1894  .  . 

63 

92 

81 



132 

•   ■   •   • 

1895  .  . 

62 

91 

79 

145 

,   , 

1896  .  . 

61 

91 

76 

133 

,   , 

1897  .  . 

62 

92 

76 

173 

, 

1898  .  . 

64 

93 

78 

159 

^   , 

1899  .  . 

68 

111 

86 

175 

,   , 

1900  .  .  . 

75 

110 

92 

165 

•   • 

1901  .  .  . 

70 

103 

91 

160 

, 

1902  .  .  . 

69 

99 

95 

165 

,   , 

1903  .  .  . 

69 

104 

96 

,   , 

1904  .  .  . 

70 

104 

95 

,   , 

1905  .  .  . 

72 

107 

98 

•   • 

1906  .  .  . 

77 

103 

— 

— 

- 

I 


STATISTICAL  DATA  427 

1  For  England,  the  figures  of  prices  are  from  Jevons  and  Sauerbeck. 
Those  from  Sauerbeck  begin  in  1852.  They  are  taken  from  the  Aldrich 
Senate  report  on  Wholesale  Prices,  1893  (I,  247),  and  from  the  Journal  of 
the  Boyal  Statistical  Society.  Those  from  Jevons  are  from  1824  to  1852 
inclusive,  and  are  taken  from  his  "  Investigations  in  (^'urrency  and  Fi- 
nance." In  order  to  make  the  tables  of  Jevons  and  Sauerbeck  continu- 
ous, Jevons's  number  for  1852  is  called  78  (i.e.,  Sauerbeck's  for  that 
year)  instead  of  65,  as  given  in  the  '-Investigations,"  and  all  the  other 
numbers  are  raised  in  the  ratio  of  78  to  65.  Jevons's  figures  are  for  forty 
commodities  ;  Sauerbeck's  are  for  forty-five. 

The  German  numbers  are  from  Soetbeer,  Heinz,  and  Conrad.  Those 
for  1851-91  inclusive,  are  from  Soetbeer,  continued  by  Heinz,  and  given 
in  the  Aldrich  report  (I,  294)  ;  those  for  1891-1906  inclusive,  are  from 
Conrad,  as  given  in  his  Jahrh'ucher,  1894-1906,  but  are  all  magnified  in 
the  ratio  of  109  to  98  in  order  to  make  the  series  continuous,  since  Heinz's 
figure  for  1891  is  109,  and  Conrad's,  98.  The  statistics  of  Soetbeer  and 
Heinz  cover  114  commodities. 

The  French  numbers  are  from  the  Aldrich  report  (I,  3.35)  founded  on 
the  figures  of  the  Commission  permanente  des  valeurs.  They  cover  only 
sixteen  articles. 

The  figures  for  the  United  States  are  those  of  Professor  Falkner  in  the 
Aldrich  report  (I,  9,  13),  the  weighted  averages  (last  method)  being  em- 
ployed. They  have  been  continued  after  1891  by  using  the  figures  of  the 
Bulletin  of  the  United  States  Department  of  Labor,  March,  1907,  p.  250. 
The  figures  of  this  report  have  all  been  reduced  in  a  fixed  ratio  in  order  to 
bring  the  initial  figure  for  1891  into  coincidence  with  the  figure,  for  that 
year,  of  the  Aldrich  report,  94. 

Those  for  India,  Japan,  and  China  are  from  the  Japanese  report  of  the 
Commission  for  investigation  of  monetary  systems,  1895.  The  writer  is 
under  great  obligations  to  Mr.  Ichi  Hara,  of  Tokyo,  for  a  copy  of  the  re- 
port, and  to  Mr.  Sakata,  of  Yale  University,  for  translating  the  tables. 

That  for  India  is  an  average  of  three  tables  which  cover  respectively 
twenty-one  articles  of  export,  sixteen  articles  of  export  priced  at  Calcutta 
and  Bombay,  and  eight  grains  at  Bombay.  That  for  Japan  is  an  average 
of  three  tables,  of  forty-two  articles  at  Tokyo,  sixteen  at  Osaka,  and 
thirty-one  articles  of  export. 

The  continuation  of  the  table  after  1895  has  been  supplied  to  me  by  Mr. 
Hitomi,  one  of  my  students,  and  is  based  on  Reports  of  the  Tokyo  Eco- 
nomic Magazine  I^blishing  Company. 

That  for  China  is  an  average  of  three  tables,  of  twenty  inland  commod- 
ities, seventeen  articles  of  export,  and  fifteen  food-stuffs  in  Shanghai. 

The  tables  for  India  were  based  on  official  statistics,  those  for  Japan 
on  information  from  guilds  and  merchants,  and  those  for  China  on  the 
reports  of  the  consuls  of  Japan  and  England  (Mr.  Jameson)  in  China. 

In  the  Japanese  report  the  prices  for  Japan  are  reduced  to  a  silver 
basis.  As  silver  was  at  a  premium  up  to  1885,  it  has  been  necessary  in 
constructing  the  above  table  to  reconvert  into  currency  by  applying  the 
premium  for  1873-85,  viz.,  4,  4,  3,  1,  3,  10,  32,  48,  70,  57,  26,  9,  5  per 
cent  respectively. 


INDEX 


Abstinence  theory  of  interest,  43- 
51 ;  crude  form  of  agio  theory 
contained  in,  54. 

Accommodation  paper,  244. 

Accumulation  of  wealth,  process  and 
causes  of,  231-235,  290;  cycles 
of,  and  distribution,  233. 

Agio  theory  of  interest,  43,  340-341  ; 
Bohm-Bawerk's  theory  called, 
53  (see  Bohm-Bawerk) ;  early 
forms  of,  in  abstinence  theories, 
and  in  Rae's,  Jevons's,  Sax's, 
and  Launhardt's  works,  54; 
author's  version  of,  87-88. 

Agriculture,  annual  cycle  in  income- 
stream  in  connection  with, 
314,  384-385.     See  Farming. 

"Aldrich  Report"  cited,  274,  319  n.», 
427. 

America,  increasing  income-streams 
exemplified  in,  304-306 ;  cycle 
of  income-stream  fluctuations 
and  rates  of  interest  in,  315. 
See  United  States. 

Andrews,  Benjamin,  quoted,  286  n.*. 

Annuities  and  the  waiting  theory  of 
interest,  46^8. 

Appreciation,  influence  of  monetary, 
on  rate  of  interest,  78  ff.,  358  IT. ; 
relation  between  rate  of,  and 
rate  of  interest  illustrated,  80- 
81 ;  of  monetary  standard,  con- 
cept of,  257  ff. ;  of  gold  during 
period  of  paper  inflation,  259— 
265 ;  theory  of,  applied  to 
periods  of  rising  and  falling 
prices,  270-285 ;  rates  of  interest 
and,  in  London,  Berlin,  Paris, 
and  New  York,  272-275;  in 
India,  Japan,  and  China,  276 ; 
of  gold  as  compared  with  silver 
as  shown  by  rates  of  interest  on 
Indian  loans,  265-270 ;  history 
of  theory  of,  and  interest,  356— 
358. 


Aristocracy,  rise  of  an,  traced, 
232. 

Aristotle,  ground  of  opposition  of, 
to  interest-taking,  4,   22. 

Australia,  loans  and  rates  of  interest 
in,  309-310. 

Average  production  period  postu- 
lated by  Bohm-Bawerk,  55 ; 
discussion  of,  56-58. 

B 

Bacon,  N.  T.,  cited,  294. 

Bagehot,  Walter,  cited,  304,  333. 

Baldwin,  cited,  333. 

Bank  of  England,   the,  240. 

Bank  loans,  imperfect  foresight 
and,   286  n.'. 

Bank  reserves  and  rate  of  interest, 
322-324. 

Banks,   function  of,   252-253. 

Basis  of  security,  210-211,  337. 

Baxter,  Robert,  quoted,  280-281. 

Bayley,  R.  A.,  cited,  421. 

Berlin,  rates  of  interest  in,  relative 
to  rising  and  falling  prices,  273, 
319,  418-421. 

Betterments,  repairs  wliich  may  be 
called,  188,  190. 

Billeter,  cited,  424. 

BimetalHsts,  287. 

Bland  Act  of  1878,  269. 

Bloch,  cited,  292. 

Bohm-Bawerk,  Eugen  von,  4  n.*,  *, 
12,  16,  38,  39;  on  "indirect 
productivity  theories,"  13  n. ; 
quoted  on  exploitation  theory 
of  interest,  40 ;  on  abstinence 
or  waiting  theory  of  interest,  43— 
45,  49  ;  deservedly  high  esteem 
for  work  of,  53  ;  at  one  point  de- 
fective, 53 ;  consideration  of 
theory  of,  53-74 ;  summary 
of  theory  of,  54-55 ;  quoted 
on  importance  of  his  "tech- 
nical" theory,  73;  author's 
tribute  to,  74;    theory  of,  mar- 


429 


430 


INDEX 


ginal  rate  of  return  on  sacrifice 
and,  163  ff. ;  on  consumption 
loans,  241  ;  mathematical 
refutation  of  theory  of,  351- 
355 ;  cited,  45  n.,  84,  88,  92  n., 
93,  98,   103,  383,  384. 

"Bohm-Bawerk  on  Rae, "  Mixter's, 
54  n.K 

Bondholders,  125 ;  freedom  of,  from 
element  of  risk,  215-216,  245, 
256  ;  and  war  loans,  239  ;  position 
of,  as  typical  creditors,  288. 

Bonds,  explicit  and  implicit  rates  of 
interest  on,  10 ;  selling  value 
dependent  on  expected  income, 
15;  risk  element  and  the  price 
of,  216 ;  issue  of,  for  war  loans, 
239;  for  public  improvements, 
240 ;  mortgage,  of  corporations, 
245  ;  explicit  and  implicit  inter- 
est of  income,  255 ;  gold,  vs. 
currency  or  coin  bonds,  259-261  ; 
rupee,  266. 

Bond  tables,  10,  260. 

Borrowing,  on  part  of  United  States, 
305. 

Borrowing  and  lending,  in  form  a 
transfer  of  capital,  in  fact  a 
transfer  of  income,  113;  equali- 
zation of  preference  rates  by, 
117-118,  231;  modification  of 
income-stream  by,  120-125;  ef- 
fect on  capital  of  modification  of 
income-stream  by,  231  ff. ; 
theory  of,  exemplified  by  issue 
of  bonds  for  pubUc  improve- 
ments, 240 ;  influence  of  un- 
equal foresight  on,  285-287 ; 
high  rate  of  interest  sometimes 
neutralized  by,  289-290.  .See 
Loans. 

Bortkiewicz,  L.  von,  cited,  58,  68 ; 
criticism  of  Bohm-Bawerk's  the- 
ory by,  72. 

Boston,   Franklin  fund  in,   238. 

Boucher,  P.  B.,  cited,  297,  423. 

Breckenridge,   R.   M.,  cited,  422. 

Brough,  William,  quoted,  275  n.^. 

Brown,  Mary  W.,  cited,  298  n.^. 

Bullock,  C.  J.,  cited,  88. 

Business  loans,  236,  240  ff. ;  con- 
trasted with  consumption  loans, 
246-250. 

Buying  and  selling,  modification  of 
income-stream  bv,  125-127,  145, 
174-175,  176,  231;  effect  on 
capital  of  modification  of  in- 
come-stream by,  231  ff. 


Calcutta,  rates  of  interest  in,  in  rela- 
tion to  price-movements,  276, 
319 ;  yearly  average  rates  of 
interest  in,  418-421. 

California,  income-stream  of,  and 
rate  of  interest,  307. 

Call  loans,  211,  244,  275,  357  n.^. 

Calvin,  right  and  wrong  interest- 
taking  according  to,  5. 

Canals  as  subject  of  investment, 
196-197. 

Cannan,  Edwin,  cited,  230,  231. 

Capital,  interest  viewed  as  repre- 
senting productivity  of,  3  (see 
Productivity  theory,  etc.)  ;  rela- 
tion between  income  and,  14—15, 
229 ;  income  produces,  not  vice 
versa,  15 ;  how  productivity  of, 
affects  rate  of  interest,  28 ; 
waiting  forms  an  increase  of,  45 ; 
rate  of  interest  not  dependent 
on,  but  on  income,  109-113; 
modifying  income-stream  by 
changing  use  of,  137  ff. ;  rate  of 
interest  is  the  ratio  between 
income  and,  216  n. ;  effect  on, 
of  modification  of  income-stream 
by  borrowing  and  lending  or 
buying  and  selling,  231  ff. ; 
accumulation  of,  290 ;  dissipa- 
tion of,  290 ;  definition  of, 
337. 

Capitalistic  method  of  production, 
191-193,  337;  and  the  rate  of 
interest,  196-197. 

Capitalists,  socialists'  view  of,  as 
robbers  of  laborers,  38—40  ;  how 
laborers  might  becoine,  41 ;  not 
robbers,  but  labor-brokers,  41— 
42 ;  entrepreneurs,  landlords, 
and  laborers  as,  230 ;  process 
of  rise  of,  traced,  231-235. 

"Capital  seeking  investment,"  the 
phrase,  126. 

Capital-value,  effect  of  income-value 
on,  13 ;  is  discounted  income, 
110;  determination  of,  through 
rate  of  interest,  229. 

Capital-wealth,  production  of  future 
income-services  by  present, 
14. 

Carver,  T.  N.,  cited,  124  n.,  126  n., 
159,  181,  184,  214,  357  n.^. 

Cassel,  cited,  196. 

Caution,  coefficient  of,  defined,  337, 
338. 


INDEX 


431 


Chance,  options  of,  178  ;  element  of, 
and  its  effect  on  rate  of  interest, 
207  ff. ;    defined,  337-338. 

Chattel  mortgages,  300. 

China,  rates  of  interest  and  appre- 
ciation for,  276  ;  effect  of  charac- 
teristic qualities  on  rate  of 
interest  in,  292 ;  small  income- 
stream  and  high  rate  of  interest 
in,  300 ;  index  numbers  of 
prices  in,  425-426.  <See  Shang- 
hai. 

Choice,  among  optional  uses  of  capi- 
tal, 137  ff. ;  will  fall  on  income- 
stream  which  has  maximum 
desirabiUty,  139,  152,389,  397; 
two  kinds  of,  of  income,  145 ; 
determined  for  individual  by 
rate  of  interest,  but  for  society 
in  general  rate  of  interest  is  in- 
fluenced by,  146—149 ;  three 
statements  of  condition  deter- 
mining, between  options,  156 ; 
effect  of  range  of,  on  rate  of 
interest,  168-175;  practical  ef- 
fect of  range  of,  175-177,  329- 
331. 

City  lots,  mortgages  on,  245. 

Civil  War,  paper  money  and  rate  of 
interest  during,  259,  280. 

Clare,  George,  cited,  324,  423. 

Clark,  J.  B.,  cited,  189,  357,  359. 

Clearing-house  certificates,  325. 

Clothing,  effect  of  rate  of  interest  on 
price  of,  226. 

Coefficient  of  caution,  337,  338. 

Coefficient  of  probabilitj',  338. 

Coefficient  of  risk,  338,  342. 

Coin  bonds,  259-261. 

Colorado,  interest  rates  of  early,  307. 

Commercial  paper,   243. 

Commodities,  definition  of,  338. 

Commodity  interest,  277-280. 

Commutation,  rate  of,  and  rate  of 
interest,  216  n. 

Composition  of  income-stream,  in- 
fluence of,  on  time-preference, 
98-99. 

Conant,  Charles  A.,  cited,  303. 

Conrad,  J.,  cited,  424,  427. 

Consvunption  loans,  so-called,  as 
opposed  to  "productive  loans," 
240-241 ;  exemplification  of, 
246-248. 

Continuous  reckoning  of  interest,  82, 
340. 

Contractual  interest.  See  Explicit 
interest. 


Corporations,  mortgage  bonds  of ,  245. 

Cost,  interest  viewed  as  representing 
a,  3-4. 

Cost-of-production  theory  of  value, 
19. 

Cost  theory  of  interest,  rate  of  in- 
terest sought  in  ratio  between 
income  from  capital  and  cost  of 
that  capital,  29 ;  labor  cost, 
33  ff. ;  abstinence  or  waiting 
theory,  43-51  ;  summary  of 
conclusions  regarding,   51-52. 

Courtois,  Alp.,  jils,  cited,  423. 

Credit  cycles,  285. 

Creditor,  position  of  bondholder  as 
the  typical,  288. 

Crop  liens,  242-243,  253-254,  315. 

Crump,  Arthur,  cited,  423. 

Cvu-rency,  depreciation  of,  and  rate 
of  interest,  259. 

Currency  bonds,  259-261. 

Cycles  of  accumulation  and  distribu- 
tion of  wealth,  233. 

D 

Day,  Clive,  cited,  232,  292  n.^. 

D'Avenel,   Viscomte   G.,   cited,   423. 

Debentures  of  corporations,  245. 

Debtor,  position  of  stockliolder  as 
the  typical,  288. 

De  Haas,  270  n.^. 

Delay,  interest-taking  justified  by, 
by  mediiBval  writers,  5,  54. 

Del  Mar,  Alexander,  theory  of  in- 
terest of,  22 ;  marginal  rate  of 
return  on  sacrifice  and  theory  of, 
161-163;  theory  of,  that  Na- 
ture should  be  reproductive, 
does  not  hold,  186. 

Depreciation,  influence  of  monetary, 
on  rate  of  interest,  78  ff. ;  rela- 
tion between  rate  of,  and  rate  of 
interest,  illustrated,  80-81 ;  of 
monetary  standard,  concept  of, 
257   ff. 

Depression,  periods  of,  due  to  in- 
equality  of   foresight,    285-287. 

Desirability,  concept  of,  88,  338. 

Discount  curve,  defined,  338. 

Discoveries,  effect  of,  on  rate  of 
interest,  203-204. 

Disservice,   definition   of,   338. 

Dis.sipation  of  capital,  290. 

Distribution  of  wealth,  application 
of  rate  of  interest  to  theory  of, 
229  ff. ;  what  is  meant  by  the 
phrase,  230 ;  classical  theory  of, 


432 


INDEX 


abandoned,  230 ;  causes  of  in- 
equality of,  231-235 ;  effect  of 
habit  on,  232-234;  cycles  of 
accumulation  and,   233. 

Dorsey,  cited,  291. 

Douglass,  William,  quoted,  356. 

Durability  of  instruments,  and  the 
rate  of  interest,  187-188,  196, 
290 ;  changes  in  regard  to,  in 
America,  305-306. 

DwelUngs,  effect  of  rate  of  interest 
on  price  of,  225-226. 


E 


Electricity,  enlargement  of  range  of 
choice  by  discovery  of,  201. 

Elliott,  E.  B.,  statistics  by,  283  n., 
419  n. 

England,  tendency  in,  of  distribu- 
tion of  wealth  to  remain  un- 
changed, 234 ;  effect  of  indi- 
vidual characteristics  on  rate  of 
interest  in,  291  ;  expenditure  on 
railways  in,  291  ;  loans  of,  in 
China,  and  effect  on  rate  of 
interest,  293 ;  postal  savings 
banks  in,  298 ;  income-stream 
and  rates  of  interest  in,  300,  310  ; 
cycle  of  income-stream  changes 
and  rates  of  interest  in,  316 ; 
index  nimnbers  of  prices  in,  425— 
426.     See  London. 

Entrepreneurs,  and  cost  theory  of 
interest,  42-43 ;  power  exerted 
by,  on  character  of  income- 
stream  of  society,  194-195 ;  as 
capitalists,  230. 

Europe,  infrequency  in,  of  changes 
in  distribution  of  wealth,  as  com- 
pared with  United  States,  234. 

Exchange,   definition  of,   339. 

Exchange  brokerage  firms,  253. 

Expectation,  rate  of  interest  is  based 
on,  213. 

Expectation  of  life,  effect  of,  on  time- 
preference,  105-106. 

Explicit  interest  (contractual  in- 
terest), defined,  5-6,  340  ;  effect 
of  risk  on  impUcit  and,  211; 
shown  to  cUffer  from  impUcit,  in 
degree  rather  than  in  kind,  255. 

Explicit  rate  of  interest.  See  under 
Interest,  rate  of. 

Exploitation,  period  of,  relative  to 
inventions,   203-204. 

Exploitation  theory  of  interest,  38-40. 

Extraction,  rate  of,  in  mining,   185. 


Falkner,  cited,  427. 

Farmers,  fluctuations  in  income- 
stream  of,  315. 

Farming,  intensive,  degree  of,  de- 
termined by  rate  of  interest,  157, 
161. 

Farms,  mortgages  on,  244-245,  308- 
309,  361-362,  363. 

Farnam,  H.  W.,  cited,  422. 

Farr,  William,  cited,  423. 

Fashion,  force  of,  333. 

Fecundity  of  plants  and  animals, 
interest  viewed  as  representing, 
3,  22-23 ;  examination  of  the 
theory,  23-27.  See  George, 
Henry. 

Feilbogen,  translation  by,  of  Bohm- 
Bawerk's  Recent  Literature  on 
Interest,  3  n. 

Fetter,  F.  A.,  criticism  by,  of  Bohm- 
Bawerk's  concept,  58;  quoted 
on  Bohm-Bawerk's  theory,  73; 
cited,  88,  128,  184,  194. 

Fines  as  a  subterfuge  for  interest- 
taking,  5,  54. 

Fisher,  Irving,  The  Nature  of  Capital 
and  Income  by,  cited,  10,  11,  12, 
17,  20,  25,  26,  30,  39  n.^,  40,  45, 
51,  77,  82  n.',  83,  88,  90,  91,  96, 
127,  138,  141,  142  n.^,  141,  154, 
168,  189,  215,  217,  225,  226,  231, 
241,  262,  348,  404 ;  articles  by, 
cited,  85,  131,  184,  276,  332,  357, 
389,  416. 

Flow,  defined,  339. 

Food,  price  of,  not  sensibly  affected 
by  rate  of  interest,  226 ;  effect 
of  scarcity  or  abundance,  on 
rate  of  interest,  301-302. 

Foresight,  effect  of,  on  rate  of  time- 
preference,  103  ff. ;  as  appUed  to 
falling  and  rising  prices,  257— 
258,  284 ;  periods  of  speculation 
and  depression  due  to  inequal- 
ity of,  285-287  ;  effect  of,  on  rate 
of  interest,  291  ff.,  334;  effect 
of  presence  or  lack  of,  in  various 
nations  and  races,  291-294; 
partly  natural  and  partly  ac- 
quired, 297-299. 

Forestry  policy,  European  and  Amer- 
ican, 27. 

France,  effect  of  foresight,  self-con- 
trol, and  regard  for  posterity  on 
rate  of  interest  in,  291 ;  effect 
of    income-stream    on    rate    of 


INDEX 


433 


interest  in,  300  ;  index  numbers 
of  prices  in,  425-426.     See  Paris. 

Franklin  funds,  238. 

Fund,  definition  of,  339. 

Furniture,  effect  of  rate  of  interest 
on  price  of,  226. 


Q 


George,  Henry,  theory  of  interest  of, 
22-23 ;  marginal  rate  of  return 
on  sacrifice  and  tlieory  of,  161- 
163 ;  theory  of,  that  Nature 
should  be  reproductive,  does  not 
hold,  186. 

Germany,  maintenance  of  rate  of 
interest  in,  313-314 ;  index 
numbers  of  prices  in,  425-426. 
See  Berlin. 

Gibbs,  H.  H.,  271. 

Giffen,  Robert,  271 ;  cited,  310,  311, 
422. 

Gold,  appreciation  and  depreciation 
of,  258-261,  335;  rate  of  in- 
terest on,  compared  with  rate 
on  silver,  265-270. 

Gonner,  E.  C.  K.,  cited,  235. 

Goodbody,   Robert,  cited,   301,   357. 

Gotha  Mutual  Insurance  Company, 
rates  of  interest  made  by,  313- 
314. 

Graziani,  cited,  358. 

Greenback  Bill,  264. 

Greenbacks.     jSce  Paper  money. 

Greene,  David  I.,  357  n.*. 

H 

Haas,  Jacob  de,  cited,  357. 

Habit,  effect  of,  on  rate  of  time- 
preference,  105 ;  effect  of,  in 
distribution  of  wealth,  232-234. 

Hadley,  A.  T.,  cited,  216. 

Hara,  Ichi,  compilation  by,  419  n., 
427. 

Hedge,  W.  B.,  cited,  422. 

Heinz,  statistics  by,  319  n.',  427. 

Heredity,  error  in  laying  stress  on 
importance  of,  as  compared  with 
environment,  298. 

Hertzka,  Theodor,  cited,  424. 

Highways,  American,  305-306. 

Hitomi,  compilation  by,  419  n.,  427. 

Holland,  qualities  of  foresight,  self- 
control,  and  regard  for  posterity, 
and  the  rate  of  interest  in,  291  ; 
effect  of  income-.strcan\  on  rate 
of  interest  in,  300. 
2  F 


Holmes,  George  K.,  on  productive 
and  consumption  indebtedness 
in  United  States,  240-241; 
cited  relative  to  mortgage  sta- 
tistics, 244  ;  cited  in  relation  to 
statistics  of  negro  and  Russian, 
294. 

Holt,  Byron  W.,  editor  of  The  Gold 
Supply  and  Prosperity,  288, 
358  n.'i;    cited,  301,  335,  357. 

Horace,  philosophy  of,  106. 

Horner,  method  of  obtaining  average 
rate  of  interest,  262  n.^,  372. 

House,  price  of  a,  the  discounted 
value  of  its  future  income,  91. 

Howell,  Price,  cited,  291. 

Hume,  David,  8. 

Hurlbert,  H.  B.,  quoted,  302-303. 


Implicit  interest  (natural  interest), 
defined,  6,  340  ;  effect  of  risk  on 
explicit  and,  211;  differs  in 
degree  rather  than  in  kind  from 
explicit  interest,  255. 

Improvements,  and  the  rate  of  in- 
terest, 190-191,  195-196;  loans 
for  public,  240  ;   railroad,  245. 

Improvidence,  loans  to  offset,  236, 
237,   246-248. 

Impure  rate  of  interest,  212-213, 
218-219. 

Income,  relation  of,  to  capital,  14- 
15  ;  produces  capital,  not  capital 
income,  15 ;  waiting  is  not,  45- 
48  ;  time-preference  the  prefer- 
ence for  early  over  late,  89  ff.  ; 
definition  of,  90-91,  339-340  ;  de- 
pendence of  time-preference  for 
each  individual  on  his,  109  ;  rate 
of  time-preference  and  conse- 
quently rate  of  interest  depend- 
ent on,  109  ff. ;  relation  be- 
tween time-preference  and,  repre- 
sented by  schedule,  113-115; 
immediate  and  remote,  consti- 
tutes difference  between  spend- 
ing and  investing,  125-126 ; 
enjoj'able  following  on  inter- 
mediate, 141 ;  net,  is  difference 
between  total  gross  income  and 
outgo,  elements  of  both  of  wliich 
are  dependent  on  rate  of  in- 
terest, 168  ff.,  241,  339  ;  effect  of 
invention  and  discovery  on,  198- 
206;  rate  of  interest  is  the  ratio 
between    capital    and,    216    n. ; 


434 


INDEX 


loans  made  to  offset  fluctuations 
in,  236,  237-238;  public  loans 
to  offset  fluctuations  in,  of 
governments,   239-240. 

Income-concept,  88. 

Income-services,  production  of  fu- 
ture, by  present  capital-wealth, 
14. 

Income-stream  (or  Income),  defini- 
tion of,  90-91,  339,  340;  de- 
pendence of  time-preference  on 
future,  92 ;  elements  which 
constitute,  93-94 ;  modification 
of,  by  borrowing  and  lending, 
120-125,  231;  graphic  repre- 
sentation of,  by  curves,  121- 
124 ;  modif  jang  bv  method  of 
sale,  125-127,  145,  i74,  176,  231 ; 
modifying  by  changing  the  use 
to  which  capital  is  put,  137  ff. ; 
the  total  final,  141 ;  capitalistic 
method  of  production  requires 
an  ascending,  191-193;  effect 
on,  of  invention,  198  ff. ;  regu- 
lation of,  by  loans,  236  ff. ;  loans 
for  regulating  fluctuations  in 
private,  237 ;  in  public,  238- 
240 ;  effect  on  rate  of  interest 
of  character  of  (size,  shape, 
composition,  and  probability), 
299  ff. 

Income-streams,  option  among,  and 
choiceV)f  one  ha\'ing  maximumde- 
sirability,  139  ff.,  389,  397 ;  choice 
among  different  optional,  shown 
to  depend  on  rate  of  interest,  145- 
149  ;  practical  effect  of  existence 
of  large  number  of,  on  rate  of 
interest,  as  balance  wheel,  175- 

177  ;    different  cases  of  optional, 

178  ff. ;  rate  of  interest  high  with 
increasing,  low  with  decreasing, 
304-306. 

Income-value,  effect  of,  on  capital- 
value,  13. 

India,  rates  of  interest  on  loans  of, 
in  gold  and  in  silver,  265-270; 
rates  of  interest  and  appreciation 
for,  276 ;  effect  of  lack  of  fore- 
sight and  negligence  on  rate  of 
interest  in,  292 ;  low  income- 
stream  and  high  rate  of  interest 
in,  300 ;  index  numbers  of 
prices  in,  425-426. 

Indians,  effect  of  characteristics  of, 
on  rate  of  interest,  292,  294. 

Indirect  productivity  theories,  13  n. 

Indorsement,  risk  reduced  by,  218. 


Industrials,   mortgages  on,   245. 

Inequalities  of  distribution  of  wealth, 
cau.ses  of,  231-235. 

Inostranietz,  cited,  292. 

Instrument,  definition  of,  340. 

Instruments,  durability  of,  290. 

Insurance,  effect  of,  on  value  of 
capital  subject  to  risks,  217. 

Insurance  company  investments,  308- 
309,  313  ;  references  for,  421-422. 

Intensive  farming,  degree  of,  de- 
pendent on  rate  of  interest,  156- 
157,  161. 

Interactions  (intermediate  services), 
30,  90,  141,  168,  340;  not  the 
cause  but  the  result  of  value, 
39  n.* ;  value  of,  derived  from 
succeeding  future  services,  91-92, 
226  ;  how  rate  of  interest  affects, 
226-227  ;  real  object  of  business 
operations  obscured  by,  241. 

Interest :  definition  of,  3,  340 ;  vari- 
ous theories  of,  3-4 ;  early  his- 
tory of  practice  of  taking,  4-6 ; 
explicit  and  implicit,  defined, 
5-6,  236,  340 ;  explicit,  depend- 
ent upon  implicit,  9 ;  question 
of  what  determines  implicit,  9 ; 
processes  of  nature  and,  22-28; 
theories  of,  based  on  cost,  29  ff.; 
labor-saving  theory  of,  35-36 ; 
socialists'  view  of,  as  extortion, 
38-39,  41,  52;  abstinence  or 
waiting  theory  of,  43-51 ;  agio 
theory,  43  ;  Bohm-Bawerk's  agio 
theory  of,  53  ff. ;  Bohm-Ba- 
werk's theory  of,  discussed,  53- 
74 ;  relation  between  apprecia- 
tion or  depreciation  and,  77  ff. ; 
distinction  between  interest  in 
terms  of  money  and  interest 
in  terms  of  goods,  84  ;  futiUty  of 
laws  against,  127-128  ;  existence 
of,  because  of  "slowness  of 
Nature,"  185-186;  shown  to 
be,  not  a  part,  but  the  whole,  of 
income,  229 ;  rent,  profits,  and 
wages  included  in,  229-230; 
theory  of,  as  applied  to  loans, 
236  ff. ;  application  of  theory  to 
crop  liens,  242-243  ;  commercial 
paper,  243  ;  accommodation  pa- 
per, 244 ;  explicit  and  implicit, 
differ  in  degree  rather  than  in 
kind,  255;  virtual,  277-280; 
commodity,  277-280 ;  history  of 
theory  of  appreciation  and,  356- 
358.  ' 


INDEX 


435 


Interest,  rate  of :  view  of,  aa  an 
index  in  a  given  community  of 
preference  for  a  dollar  of  present 
over  a  dollar  of  future  income, 
3,  88;  "supply  and  demand" 
explanation  of,  6-7 ;  ' '  use  of 
money "  explanation  of,  7-9 ; 
theory  that  quantity  of  money 
in  circulatioil  governs,  8 ;  em- 
phasis to  be  placed  on  distinc- 
tion between  implicit  and  ex- 
plicit, 10-11 ;  existence  of  im- 
plicit in  bonds,  notes,  land,  etc., 
in  all  instruments  of  wealth, 
and  in  the  value  of  every  capital- 
good,  10-11;  cannot  be  deduced 
from  ratio  of  income  from  capital 
to  value  of  that  capital,  14-15 ; 
futility  of  raising,  by  raising 
productivity  of  capital,  15-16 ; 
the  same  objections  apply  in 
the  "use"  theories,  16  ff. ; 
Henry  George's  theories  about, 
22-23 ;  viewed  as  consisting  in 
the  average  rate  of  growth  of 
animals  and  plants,  23  ;  conclu- 
sions concerning  productivity 
theory  and,  28  ;  how  productiv- 
ity of  capital  does  affect,  28 ; 
cost  theory  of,  defined,  29 ; 
viewed  as  a  wage  for  the  labor 
of  producing  capital  (exploita- 
tion theory),  38-40  ;  relation  be- 
tween, and  monetary  standard 
in  which  it  is  expressed,  77  ff. ; 
relation  between  rate  of  appre- 
ciation or  depreciation  and, 
illustrated,  80-81 ;  the  number 
expressing,  depends  on  stand- 
ard of  value  in  which  present 
and  future  goods  are  expressed, 
82  ff. ;  always  relative  to  stand- 
ard in  which  expressed,  84 ;  no 
absolute  standard  of  value  for 
reckoning,  84-86 ;  determining 
the,  87  ff. ;  basis  of,  on  time- 
preference,  88  (see  Time-prefer- 
ence) ;  consideration  of  relation 
between  rates  of  preferences  and, 
117  ff. ;  four  conditions  which 
determine,  132-133;  choice 
among  optional  income-streams 
governed  by,  145 ;  change  in, 
results  in  change  of  choice  of 
income-streams,  146,  168  ff. ; 
determines  choice  of  individual 
among  optional  income-streams, 
but  for  society  at  large  is  influ- 


enced by  the  existence  of  options, 
146-149 ;    six   conditions  which 
determine,  150  ;  choice  of  option 
whose  marginal  rate  of  return  on 
sacrifice  is   equal   to,    158,    159 ; 
effect  on,  of  range  of  choice  be- 
tween options,    168-175 ;    effect 
of,  on  wages  of  labor,  169-170; 
change  in,  will  affect  all  income- 
streams      flowing      from     given 
instruments     of     capital,      171  ; 
practical  effect  on,   of  range  of 
choice,    175-177 ;    effect   of,    on 
speculation,     179-180 ;      arising 
from     "slowness     of     Nature," 
185 ;     waterworks,    canals,    irri- 
gation systems,  improvement  of 
railways,     etc.,     and,     196-197 ; 
effect  of  invention   on,    198   ff. ; 
temporary    nature    of    effect    of 
invention     on,     203-204 ;      ele- 
ment of  uncertainty  in  income 
and,  207  ff. ;    based  on  expecta- 
tion, 213  ;  and  rate  of  commuta- 
tion, 216  n. ;    role  played  by,  in 
the    theory    of    prices,    225    ff. ; 
influence  on,  of  changes  in  the 
monetary     standard,      257-288, 
356    ff. ;     tables    showing    com- 
parative rates  realized  on  gold 
and   currency  bonds,   260,   262 ; 
comparison  of  rates  on  gold  and 
on    silver,    265-270 ;  periods    of 
rising    and     falling   prices    and, 
270-285;   relatively  high    when 
prices  are  rising,  low  when  fall- 
ing, 277 ;    loans  as  an  offset  to 
high,  289-290  ;  manner  in  which 
nature   of   the   individual   influ- 
ences,  290-299;    effect  of  fore- 
sight, self-control,  and  regard  for 
posterity  on,  291  ff. ;    effect  on, 
of    character    of    income-stream 
(size,    shape,    composition,    and 
probability),   299  ff. ;    inductive 
refutation  of  money  theory  of, 
317-326;     table   of,    in   relation 
to    high    and    low    prices,    319; 
quantity    of    money    and,    320- 
322 ;     bank   reserves   and,    322- 
324 ;     definition    of,    in    various 
senses,    340-341 ;    formula    con- 
necting  rates  in   two    diverging 
standards,  358-360  ;  yearly  aver- 
age   rates    in    London,    Berlin, 
Paris,  etc.,  418-421. 
Interest-taking,  early  laws  and  prac- 
tices concerning,  4-6 ;    not  pre- 


436 


INDEX 


vented  by  prohibiting  loan  con- 
tracts, 127. 

Intermediate  services.  See  Inter- 
actions. 

Invention,  economic  effect  of,  198  ff. ; 
temporary  nature  of  effect  of, 
on  rate  of  interest,  203-204 ; 
the  basis  of  progress  in  civiliza- 
tion, 205 ;  conditions  for  most 
rapid  multiplication  of,  205- 
206  ;  speculation  following,  212- 
213 ;  effect  of,  on  time-shape  of 
income-streams,  313 ;  progress 
of,  and  its  bearing  on  rate  of  in- 
terest, 334. 

Inventors,  tribute  to,  206. 

Investing,  defined  as  purchase  of 
right  to  remote  enjoyable  in- 
come, 125-126,  341. 

Investment,  period  of,  in  connection 
with  inventions,  203-204  ;  effect 
of  risk  on  rate  of  interest  in 
cases  of  imsafe,  212-213;  in 
cases  of  safe,  213-215. 

Investments  of  insurance  companies, 
308-309,  313-314,  421-422. 

Ireland,  small  income-stream  and 
high  rate  of  interest  in,  300-301. 

Irrigation  works,  as  subject  of  in- 
vestment, 197. 


Jameson,  consular  report  of,  427. 

Japan,  rates  of  interest  and  apprecia- 
tion for,  276 ;  peace  loan  for, 
313 ;  yearly  average  rates  of 
interest  in,  418-420;  index 
numbers  of  prices  in,   425-426. 

Java,  debt  servitude  in,  232  ;  rate  of 
interest  in,  as  affected  by  lack 
of  foresight  and  negligence,  292. 

Jevona,  W.  Stanley,  agio  theory  in 
work  of,  54,  74 ;  Bohm-Bawerk 
on,  73  ;  cited,  2.52,  301-302,  330, 
422,  427;  De  Haas'  criticism  of, 
270  n.2 ;  tables  of,  277,  319  n.' ; 
quoted,  281. 

Jews,  interest-taking  between,  for- 
bidden by  Mosaic  laws,  4  ;  effect 
of  characteristic  qualities  on 
rate  of  interest  among,  291  ; 
low  preference  rate  among,  295  ; 
natural  and  traditional  tenden- 
cies of,  298. 

Johnson,  Joseph   F.,  cited,  358. 

Jones,  Senator,  357  n.*. 

Juglar,  cited,  286  n.'. 


K 


Kahn,  J.,  cited,  424. 
Kellogg,  Dr.  J.  H.,  298  n.«. 
Kellogg,  Mrs.  J.  H.,  298  n.». 
Kemmerer,   E.  W.,  cited,  301. 
Kiaer,  A.  N.,  cited,  425. 
Kinley,  David,  cited,  239. 
Klondike,  high  interest  rates  in  the, 

307. 
Korea,  effect  of  risk-element  on  rate 

of  interest  in,  302-303. 


Labor,  cost  of,  an  important  ele- 
ment in  income-accounts,  169- 
170;  bearing  of,  on  choice  be- 
tween uses  of  capital  affording 
immediate  and  those  affording 
remote  returns,  193-195  ;  wages 
of,  as  affected  by  rate  of  interest, 
228-229;  defined  as  outgo  in 
the  form  of  human  exertion, 
341. 

Labor  cost,  in  cost  theories  of  in- 
terest, 33  ff. 

Laborers,  rate  of  interest  and  wages 
of,  169-170,  228 ;  may  be  small 
capitalists,  230. 

Labor-saving  theory  of  interest,  35- 
36. 

Land,  as  an  instrument  of  wealth, 
implies  a  rate  of  interest,  11  ; 
in  Turgot's  explanation  of  im- 
plicit interest,  11-12;  view  of, 
as  source  of  all  human  revenue, 
12 ;  degree  of  intensiveness  of 
cultivation  of,  governed  by  rate 
of  interest,  157,  161  ;  speculation 
in,  and  effect  of  rate  of  interest 
on,  180  ;  effect  of  rate  of  interest 
on  price  of,  225;  mortgages  on, 
244-245,  308-309;  defined  as 
wealth  which  is  part  of  the 
earth's  surface,  341. 

Landlords  as  capitalists,  230. 

Land  mortgages,  244-245,  308-309, 
363 ;  reference  for  information 
on,  421. 

Landry,  Adolphe,  cost  theory  of 
interest  of,  37-38,  161  ;  criticism 
of  Bohm-Bawerk's  theory  by, 
72;  cited,  84,  92  n.,  159,  181. 

Lanin,  E.  B.,  cited,  292. 

Laspeyres,  E.,  cited,  424. 

Launhardt,  agio  theory  in  work  of, 
54,  74  ;  liohm-Bawerk  on  views 
of,  73. 


INDEX 


437 


Law  of  decreasing  returns  for  addi- 
tional sacrifice,  33,  157. 

Laws  against  interest-taking,  futility 
of,  127-128. 

Le  Bon,  cited,  333. 

Lending,  limitation  of,  due  to  risk, 
117;  difference  of  risk  indicated 
by,  216.  See  Borrowing  and 
lending  and  Loans. 

Levy,  B.  R.  G.,  cited,  322. 

Lexis,  cited,  58. 

Liegeois,  J.,  cited,  423. 

Life,  expectation  of,  and  time- 
preference,    105-107. 

Life  insurance,  108. 

Life  insurance  companies.  Western 
investments  of,  308-309. 

Loans  (loan  contracts),  a  means  of 
equalizing  rate  of  time-prefer- 
ence and  rate  of  interest,  118- 
125 ;  interest-taking  not  pre- 
vented by  prohibiting,  127 ; 
effect  of  risk  on,  211-212; 
classification  of,  236 ;  private, 
237-238  ;  public,  238-240  ;  pub- 
lic, to  offset  fluctuations  in 
revenue  and  expenses,  239-240 ; 
for  public  improvements,  240 ; 
business,  240  ff. ;  productive  and 
consumption,  240-241 ;  short  or 
periodic,  242-244 ;  long-time 
or  permanent,  244-245 ;  con- 
sumption, 246-248 ;  productive, 
246-248 ;  brokerage  concerns 
for  handling  (banks,  trust  com- 
panies, etc.),  253;  sale  of,  254; 
high  interest  rate  neutralized  by, 
289-290;  English,  in  China,  and 
effect  on  rate  of  interest,  293 ; 
high  rate  of  interest  on  risky, 
302 ;  low  rate  on  safe,  303 ; 
rates  on,  in  new  Western  farm- 
ing countries,  308-309 ;  caused 
by  misfortune,  311-312;  war, 
312-313;    panic,   324-326. 

Locke,  attempted  explanation  of 
interest  by,   6. 

London,  rates  of  interest  in,  rela- 
tive to  rising  and  falling  prices, 
271-273,  282,  319;  yearly 
average  rates  of  interest  in, 
418-421. 

Longfield,  cited,   301. 

Lowry,  Dwight  M.,  cited,  22  n. 

Lucam,  W.  von,  cited,  424. 

Lumbering  communities,  cycle  of 
interest  rates  in,  308. 

Luxury,  habit  of,  233. 


M 


Managing,  cost  of,  42-43,  51. 

Manufacturers,  fluctuations  in  in- 
come-stream of,  315. 

Marginal    desirability,    defined,    338. 

Marshall,  cited  and  quoted,  84, 
287  n.,  358,  359,  417. 

Menger,  Karl,  cited,  212. 

Metchnikoff,  cited,    106. 

Michigan,  lumbering  and  rates  of 
interest  in,  308. 

Military  purposes,  loans  for,  238- 
239,  312-313. 

Mill,  J.  S.,  cited,  324,  357. 

Mining,  rate  of  extraction  in,  185. 

Mining  communities,  rates  of  interest 
in,  306-308. 

Misfortune,  loans  to  offset,  236,  237, 
248-251 ;  public  loans  to  offset 
(war  loans),  238-239,  312-313. 

Mixter,  C.  W.,  editor  of  Rae's  So- 
ciological Theory  of  Capital, 
37  n.\  54  n.\  74. 

Monetary  standard,  appreciation  and 
depreciation  of,  257  ff. 

Money,  theory  that  quantity  of,  in 
circulation,  governs  rate  of  in- 
terest, 8,  14,  19,  320-322;  the 
standard  of  value  usually  chosen 
to  express  rate  of  interest,  77 ; 
influence  of  appreciation  or 
depreciation  of,  on  rate  of  inter- 
est, 78  ff. ;  represents  capital- 
ized income,  122;  the  most  sala- 
ble of  properties,  212;  inductive 
refutation  of  money  theory  of 
rate  of  interest,  317-326. 

Mora  (delay),  interest-taking  justi- 
fied by,  5,  54. 

Mormons  as  laborers  who  became 
capitalists,  41. 

Mortgage  companies,  253. 

Mortgages,  on  real  estate,  244-245, 
308-309,  363;  chattel,  300; 
reference  for  information  con- 
cerning land  mortgages,  421. 

Moses,  Bernard,  cited,  259. 

Mullhall,  M.  G.,  cited,  423. 


N 


Natural  interest.  See  Implicit  in- 
terest. 

Nature,  slowness  of,  and  effect  on 
existence  of  interest,  185-186; 
productivity  of,  and  interest, 
186-187. 


438 


INDEX 


Negroes,  effect  of  characteristics  of, 
on  rate  of  interest,  292,  294 ; 
reversal  of  characteristics  by 
training,  298. 

Net  income,  defined,  168  ff.,  241,  339. 

Nevada,  cycle  of  rates  of  interest  in, 
308. 

New  England  Mutual  Life  Insurance 
Company,  report  of,  cited,  421. 

Newmann,  M.,  cited,  424. 

Newmarch,  cited,  284  n.,  423. 

New  York,  rates  of  interest  in,  rela- 
tive to  rising  and  falling  prices, 
275,  283,  319;  yearly  average 
rates  of  interest  in,  418-421. 

Norton,  John  P.,  cited,  335,  358, 
425. 

Notes,  explicit  and  implicit  rates  of 
interest  on,  10.  See  Bonds  and 
Mortgages. 


O 


Offspring.     See  Regard  for  posterity. 

Ophelimity,  88  n.'. 

Options,  among  various  income- 
streams,  139  ff.,  341 ;  rate  of 
interest  determines,  for  indi- 
vidual, but  for  society  at  large 
existence  of  options  influences 
rate  of  interest,  146-149  ;  eligible 
and  ineligible,  150,  397  ;  condition 
determining  choice  between,  156  ; 
choice  among,  where  indefinite 
in  number,  156-158  ;  three  chief 
kinds  of,  178;  of  versatility, 
178;  of  chance,  178-179;  special 
case  of  trade,  the  ordinary  use 
of  the  word  "option,"  179; 
consideration  of,  among  em- 
ployments of  capital  winch  differ 
in  size  and  time-shape,  179  ff. ; 
special  cases  of,  applying  to 
durable  instruments  of  wealth, 
180  ff. ;  when  quantity  of  in- 
come is  definitely  fixed,  180- 
184 ;  when  income  is  fixed,  but 
comes  slowly,  185-186  ;  of  mak- 
ing renewals  and  repairs,  188- 
190  ;  of  betterments,  190-191 ; 
different  methods  of  production 
and,  191-193  ;  involving  human 
capital,  labor,  193-195;  certain 
untouched,  beyond  the  margin 
of  choice  (waterworks,  canals, 
railways,  etc.),  196-197;  intro- 
duction of  new,  by  invention  and 
di.'^coveries,   198  ff. 


Orchard,  as  an  example  of  capital- 
value,  13. 

Outgo,  waiting  is  not,  45-48 ;  defined 
as  negative  income,  341. 


Palgrave,  R.  H.  I.,  cited,  316,  422. 

Panics,  financial,  324-326. 

Paper  money,  and  rate  of  interest, 
259 ;  rates  on,  compared  with 
rates  on  coin,  260-265. 

Paraguay,  lack  of  foresight  among 
Indians  of,  294. 

Pareto,  curves  of  distribution  of 
income  of,  231. 

Paris,  rates  of  interest  in,  relative  to 
rising  and  falling  prices,  274, 
319 ;  yearly  average  rates  of 
interest  in,  418-421. 

Partial  payments,  considered  in  rela- 
tion to  appreciation  and  in- 
terest,  361-363. 

Patents,  198,  206. 

Pawn  shops,  209-210,  300. 

Peasantry,  process  of  decline  of 
individuals  into  a,  232  ;  personal 
characteristics  of,  and  effect  on 
rate  of  interest,  292,  294. 

Perishability  of  instruments,  290. 

Personal  equation,  influence  of,  on 
time-preference,  103  ff. 

Philadelphia,  Franklin  fund  in,  238. 

Philippines,  small  income-streams 
and  high  rate  of  interest  in,  300- 
301. 

Physiocrats,  12. 

Pigou,  A.  C,  cited,  84  n.*. 

Plehn,  Carl  C,  quoted,  307;  cited, 
422. 

Poor,  debtor-class  not  composed  of 
the,  288 ;  borrowing  among  the, 
299-300,   311-312. 

Population,  effect  of  increase  of,  on 
time-preference,  108. 

Postal  savings  banks,   EngUsh,  298. 

Posterity,  influence  of  regard  for,  on 
time-preference,  107—109 ;  bear- 
ing of  regard  for,  on  rate  of 
interest,  296-299,  334. 

Poverty,  effect  of,  on  time-prefer- 
ence, 94-95  ;  high  rate  of  inter- 
est due  to,  294-295. 

Powers,  H.  H.,  357  n.». 

Preference  rate,  equalization  of,  by 
borrowing  and  lending,  or  buj^ing 
and  selhng,  117-118,  125-127, 
231;    definition  of,  342. 


INDEX 


439 


Preferred  stock,  implicit  vs.  explicit 
interest  of,  255. 

Premium  concept  of  interest,  53, 
340.     See  Agio  theory. 

Preparatory  service,  90. 

Price,   Bonamy,   quoted,   281-282. 

Prices,  r61e  played  by  rate  of  interest 
in  theory  of,  225  ff. ;  rising  and 
falling,  and  theory  of  apprecia- 
tion, 270  ff. ;  market  rates  of 
interest  in  relation  to  high  and 
low,  318-320  ;  index  numbers  of, 
in  seven  countries,  425-426. 

Price  sense  of  rate  of  interest,  340,  341 . 

Primogeniture,  law  of,  and  effect  on 
distribution  of  wealth,  234. 

Probability,  element  of,  in  time- 
preference,  94,  99-102 ;  coeffi- 
cient of,  338. 

Productive  loans,  so-called,  240  ff., 
246-248. 

Productivity,  physical  and  value, 
defined,  341. 

Productivity  theory  of  interest,  3 ; 
Turgot's  theory  a  particular 
species  of,  12;  confusion  by,  of 
physical-productivity  and  value- 
return,  12-14 ;  fact  overlooked 
by,  that  income  produces  capi- 
tal, not  capital  income,  14-15 ; 
futility  of,  shown  by  observing 
effect  of  change  of  productivity 
on  capital- value,  15-16;  "use 
theory  ' '  a  special  and  improved 
form  of,  16;  Henry  George's 
statement  of  the  organic,  22-23 ; 
examination  and  refutation  of 
the  organic,  23-27 ;  rate  of 
interest  sought  in  ratio  between 
income  from  capital  and  value  of 
that  capital,  29 ;  mathemati- 
cally considered,  347-350. 

Profits,  included  in  "interest,"  229- 
230. 

Property,  89,  341. 

Property-right,  valuation  of  every, 
involves  interest,  127  ;  complete 
and  partial,  defined,  341. 

Prosperity,  periods  of  so-called,  288. 

Pseudo-rate  of  interest,  212-213, 
218-219. 

Public  improvements,  loans  for,  236, 
240. 


Q 


Quantitv  of  Tiioney  and  rates  of  in- 
terest, 8,  14,  19,  317,  320-322. 


R 


Rae,  John,  cost  theory  of  interest  of, 
37-38,  74,  159  ;  Bohm-Bawerk's 
comments  on,  54  n.' ;  quoted  re- 
garding foresight,  104 ;  quoted 
relative  to  expectation  of  life  and 
time-preference,  106-107;  de- 
fect in  analysis  of  interest  of, 
112  n. ;  on  time-preferences  of 
individuals  and  relation  to  rate 
of  interest,  117;  treatment  by, 
of  subject  of  economic  effect  of 
invention,  203  ;  contribution  of, 
to  subject  of  philosophical  the- 
ory of  distribution,  231  ;  quoted 
concerning  the  Dutch,  291-292; 
on  the  Chinese,  292-293;  on 
disregard  for  posterity  of  ancient 
Romans  of  degenerate  days, 
296-297 ;  on  lack  of  durable  in- 
struments in  America,  305-306 ; 
cited,  88,  103,  106,  108,  302, 
332,   333. 

Raguet,  Currency  and  Banking  by, 
quoted,  259. 

Railways,  improvement  of,  197 ; 
inventions  which  led  to,  and 
effect  on  income-stream  of  so- 
ciety, 201 ;  mortgage  bonds  and 
debentures  of,  245  ;  expenditure 
on,  in  England,  291 ;  charac- 
teristics  of  American,   306. 

Railway  securities,  reference  for  data 
concerning,  421. 

Range  of  choice,  168  ff.,  329-331. 

Rate  of  commutation,  216  n. 

Rate  of  extraction  in  mining,  185. 

Rate  of  interest.  iSee  Interest,  rate 
of. 

Rate  of  preference.  See  Preference 
rate. 

Rate  of  retvirn  on  .sacrifice,  153  ff., 
342;     marginal,    158,    159,    342. 

Real  estate  mortgages,  244-245,  308- 
309,  363  ;  reference  for  informa- 
tion on,  421. 

Reese,  Michael,  307. 

Regard  for  posterity,  and  time-pref- 
erence, 107-109 ;  bearing  of,  on 
rate  of  interest,  296-299,  334. 

Rent,  dependence  of,  on  rate  of 
interest,  227;  included  in  "in- 
terest," 229-2.30. 

Rent  purchase,  device  of,  128. 

Repairs  and  renewals,  options  of 
making,  188,  190;  and  the  rate 
of  interest,  195-196. 


440 


INDEX 


Return  on  sacrifice,  rate  of,  153  ff., 
342;   marginal  rate  of,  158,  159. 

Ricardo,  and  tlie  fallacy  that  value 
of  the  product  equals  its  cost,  39. 

Risk,  influence  of,  on  time-preference, 
99-102 ;  limitation  of  lending 
due  to,  117 ;  effect  of  element  of, 
on  rate  of  interest,  207  ff.,  302- 
304  ;  the  greater  the,  the  higher 
the  basis  on  which  security  will 
sell,  210-211 ;  effect  of,  on  im- 
pure rate  of  interest  (i.e.  rate 
on  unsafe  investments),  212- 
213 ;  effect  on  safe  investments, 
213-215 ;  assumption  of,  by 
stockholders  in  corporations, 
215,  256;  insurance  and  its 
effect  on  capital  subject  to,  217 ; 
effect  of  speculation  in  reducing, 
217 ;  summary  of  disturbances 
caused  by  introduction  of  ele- 
ment of,  217  ff. ;  influence  of,  on 
difference  between  explicit  and 
implicit  interest,  255-256  ;  con- 
stitutes real  difference  between 
stocks  and  bonds,  256 ;  coeffi- 
cient of,  338,  342. 

Robbins,  G.  P.,  compilation  by,  283n., 
419  n. 

Rodbertus,  40  ;   cited,  424. 

Romans,  interest-taking  between, 
prohibited  by  Roman  law,  4 ; 
disregard  for  posterity  among 
ancient,  of  degenerate  days, 
107-108,  296-297. 

Roscher,  illustration  borrowed  from, 
33. 

"Roundabout  process,"  B6hm-Ba- 
werk's,  55,  66,  71-73,  163-164. 

Rupee  paper,  266. 

Russia,  rate  of  interest  among  peas- 
antry of,  232,  292,  294. 


S 


Sacrifice,  rate  of  return  on,  153  ff. ; 
law  of  decreasing  returns  for 
additional,  157  ;  marginal  rate  of 
return  on,  158,  159 ;  definition 
of,  342. 

Sailors,  influence  of  risk  on  time- 
preference  of,  102. 

Sakata,  translation  by,  419  n., 
427. 

Sale,  method  of.  See  Buying  and 
selling. 

Salmasius,  attempted  explanation  of 
interest  by,  6. 


San  Francisco,  mortgage  rates  in, 
307 ;  earthquake  in,  and  loans 
arising  from,  312. 

Sauerbeck,  tables  of,  319  n.',  418  n., 
427. 

Saugrain,  Gaston,  cited,  423. 

Saving,  phenomenon  of,   126. 

Savings  banks,  function  of,  252- 
253 ;  postal,  in  England,  298. 

"Saving  capital  out  of  income,"  the 
phrase,  defined,  126. 

Sax,  agio  theory  in  work  of,  54,  74. 

SchmoUer,  Gustav,  cited,  424. 

Scotch,  natural  and  acquired  ten- 
dencies of,  298. 

Scotland,  foresight,  .self-control,  and 
regard  for  posterity,  and  the  rate 
of  interest  in,  291. 

Scott,  translation  by,  of  Bohm- 
Bawerk's  Recent  Literature  on 
Interest,  3  n. 

Seaman,  J.  F.,  419  n. 

Seasons,  changes  in  income-stream 
due  to  succession  of,  314-315. 

Securities,  investments  in.  See 
Stocks  and  Bonds. 

Self-control,  effect  of,  on  rate  of 
time-preference,  105  ff. ;  partly 
natural  and  partly  acquired, 
297-299  ;  influence  of,  on  rate  of 
interest,  334. 

Seligman,  E.  R.  A.,  cited,  297; 
quoted,  424. 

Selling.     See   Buying   and   selling. 

Senior,  abstinence  theory  of,  54. 

Services,  89 ;  two  kinds  of,  inter- 
mediate and  final,  226 ;  effect 
of  rise  or  fall  of  rate  of  interest 
on,  226-227 ;  enjoyable  objec- 
tive, defined,  342 ;  intermediate, 
see  Interactions. 

Shanghai,  rate  of  interest  in,  in  rela- 
tion to  price-movements,  276, 
293,  319;  yearly  average  rates 
of  interest  in,  418-421. 

Sherman  Act  of  1890,  269. 

"Shirt  sleeves  to  shirt  sleeves  " 
adage,  233. 

Silver,  appreciation  and  deprecia- 
tion of,  258  ;  rate  of  interest  on, 
compared  with  rate  on  gold, 
265-270. 

Simcox,  quoted  on  rate  of  interest  in 
China,  293. 

Single- tax  advocates,  4  n.'. 

Smart,  William,  translation  of  Bohm- 
Bawerk's  Capital  and  Interest 
by,  3. 


INDEX 


441 


Socialists,  and  the  view  of  rate  of 
interest  as  a  wage  for  labor  of 
producing  capital  (exploitation 
theory),  38-40,  52;  where  mis- 
take is  made  by,  235. 
Soetbeer,    Adolf,    statistics   by,    273, 

319  n.»,   423,   427. 
Sombart,  cited,  424. 
Speculation,  effect  of  rate  of  interest 
on,     179-180;      following     new 
inventions,    212-213;    effect   of, 
in   reducing  risks,   217 ;    u.se   of 
loans  in,   244 ;    periods   of,   due 
to  inequality  of  foresight,  285- 
287. 
Spending,    defined    as    purchase    of 
right    to    immediate    enjoj'able 
income,  126,  342. 
Spruce  timber,  two  acres  of,  for  one 

edition  of  newspaper,  27. 
Standard  deviation  of  rates  of  inter- 
est, 279,  283. 
Standard  of  value,  no  absolute,  ex- 
cept for  a  particular  individual, 
84-86. 
Standardizing  of  income,  17-18. 
Stockholders,      office      of,     as      risk 
takers,    215-216;    as    borrowers 
in    cases    of   loans    by    corpora- 
tions, 245  ;  are   at  present  time 
the  tj-pical  debtors,  288. 
Stocks,  explicit  and  implicit  rate  of 
interest    on,    10;     selling    value 
dependent  on  expected  income, 
15 ;    risk  element  and  the  price 
of,  216. 
Streuber,  W.  J.,  cited,  424. 
Sumner,  cited,  259,  286  n.». 
Supply  and  demand,  explanation  of 
rate  of  interest  by,   6-7 ;    ques- 
tion of  what    constitutes,  9 ;   in 
Turgots'  explanation  of  implicit 
interest,   11-12;   dependence    of 
rate  of  wages  on,  228. 


Tarde,  G.,  cited,  333. 

Taussig,  F.  VV.,  cited,  58. 

Taylor,  F.  M.,  compilation  by,  418  n., 
422. 

Technical  superiority  of  present 
goods,  Bohm-Hawerk's  theory 
of,  55,  58-74  ;  business  loans  set 
down  as  due  to,  241. 

Technique  of  production,  Bohm- 
Bawerk's,  marginal  rate  of  re- 
turn on  sacrifice  and,   159. 


Thrift,  habit  of,  233  ;    bearing  of,  on 

rate  of  interest,  334. 
Time-preference  in  theory  of  interest, 
3,   88,   342;    Rae's   and    Bohm- 
Bawerk's    terms    approximating 
to,  88 ;    summed  up  as  a  prefer- 
ence   for    early    over     late     in- 
come,    89 ;      four    elements    on 
which    dependent,  94;    depend- 
ence of,  on  size  of  income,  94- 
95  ;   influence  on,  of  distribution 
of  income  in  time,  95-98 ;   influ- 
ence of  composition  of  income- 
stream  on,  98-99 ;    influence  of 
risk  on,  99-102  ;   dependence  of, 
on  income,  103,  109 ;    effect  on, 
of  foresight,   self-control,   habit, 
expectation  of  life,  and  interest 
in  the  lives  of  other  persons,  103- 
109  ;    relation  between,   and  in- 
come,  represented  by  schedule, 
113-115;    law  of,   331-332. 
Time-shape    of    income-stream,    95- 
98,    342-343;     modification    of, 
by  borrowing  and  lending,  118- 
124 ;      impress     on,     of     choice 
among  income-streams,   141   ff . ; 
dependence  of  rate  of  interest  on, 
304-306. 
Tokyo,  rates  of  interest  in,  in  relation 
to    price-movements,    276,    319; 
yearly  average  rates  of  interest 
in,  418-421. 
Tooke,  cited,  282,  284  n.,  423. 
Trade  options,  178-179. 
Training,  influence  of,   on  habits  of 
foresight,  self-control,  etc.,  298- 
299. 
Trust  companies,  function  of,  253. 
Tsuboya,  Zenshiro,  history  of  Japan 

by,  419  n. 
Turgot,    attempted    explanation    of 
implicit  interest  by,   11-12,   23. 


U 


Uncertainty  of  income  and  the  rate 
of  interest,  207  ff.     See  Risk. 

United  States,  cyclical  movement  of 
accumulation  and  distribution  of 
wealth  in,  233-234  ;  increasing  in- 
come-streams in, 304-306 ; index 
nimibers  of  prices  in,  425-426. 

"Use"  theory  of  interest,  3,  4  n.^, 
7-9,  16-20. 

Usury,  futility  of  mediaeval  laws 
against,  128. 

Utility,  88  n.»,  338. 


442 


INDEX 


Value,  defined,  343. 

Variability,  mean,  of  rates  of  interest, 

279,   283. 
Versatility,  options  of,  178. 
Virtual  interest,  277-280. 

W 

Wages,  effect  of  rate  of  interest  on, 
169-170,  228-229;  included  in 
"interest,"  229-230. 

Waiting,  cost  of,  4,  50. 

Waiting  theory,  43-51  ;  crude  form 
of  agio  theory  contained  in,  54. 

War  loans,  238-239,  312-313. 

Waterworks,  loans  for,  240 ;  as  sub- 
ject of  investment,   196. 

Wealth,  89,  343. 

Weighted  arithmetical  mean,  Bohm- 
Bawerk's,  56-58,  351-352. 


Wheat,  speculation  in,  180 ;  price 
of,  and  rate  of  discount,  301- 
302,  361. 

Williams,  F.  W.,  419  n. 

Winter,  G.,  cited,  424. 

Wood-pulp,  23-27. 


Yearly  average  rates  of  interest,  418- 
421. 

Years'  purchase,  a  rate  of  interest 
implied  by  sale  of  land  on  basis 
of  a  number  of,  11 ;  in  Turgot's 
explanation  of  implicit  interest, 
11-12. 


Z 


Zartman,  L.  W.,  Investments  of  Life 
Insurance  Companies  by,  cited, 
309,  310,  314,  422. 


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